Texas Instruments Tl-89, Tl-92 Plus User guide

TI-89
TI-92 Plus

A

C

A

TI.89 Shortcut Keys

General

¥O
2a

List of Flash applications

Toggle between last two chosen
applications or split screens

¥|, ¥«
¥¸
¥C, ¥D

Lighten or darken contrast

Calculate approximate answer

Move cursor to top or bottom
(in editors)

¤ C, ¤ D
¤ A, ¤ B
2C, 2D

Scroll tall objects in history

Highlight left or right from cursor

Page up or page down
(in editors)

2A, 2B

On-screen Keyboard Map (

Move cursor far left or far right

¥^

)

Press N to exit the map.

The keyboard map displays shortcuts that are
not marked on the keyboard. As shown
below, press ¥ and then the applicable key.

¥Á
¥c

ƒ

ccess Greek letters

(see next column)

¥d
¥b

¥e
¥Í
¥

1 – ¥9

¥ p
¥^
¥ §
¥´

(comment)

¦

Copy graph coordinates to

sysdata

!

(factorial)

Display

FORMATS

Run programs
through

&

kbdprgm9()

(append)

dialog box

kbdprgm1()

On-screen keyboard map

@

Turn off unit so that it returns
to current application the
next time you turn it on

¥µ
¥¶
¥·

(zero)



‚

Copy graph coordinates to
Home screen history

Alpha Rules

j
¤

2™

¤j
j

Type one lowercase letter

Type one uppercase letter

Lowercase alpha lock

Uppercase alpha lock

Exit alpha lock

3D Graphing

, D, A,

«, |

X, Y, Z

µ
Í
p

B

nimate graph

Change animation speed

View along axis

Return to original view

Change graph format style

Expanded/normal view

Greek Letters

¥c

To access the Greek
character set

¥cj

+ letter To access lowercase Greek

letters. Example:

ω

¥c¤

¥cj

[W]

displays

+ letter To access uppercase Greek

letters. Example:

¥c¤

[W]

displays

Ω

If you press a key combination that does not
access a Greek letter, you get the normal
letter for that key.

ψξ

ζτ

XYZT

β

α

ABCDE

Γ

γ

φ

FGH I J

λ

KLMNO

Π

π

PQRSU

Ω

ω

VW

∆

ε

δ

µ

Σ

ρ

σ

TI-89
TI-92 Plus

Guidebook

for Advanced Mathematics
Software Version 2.0

U.S. Patent No. 4,405,829 Licensed Exclusively By RSA Data Security, Inc.

© 1999 by Texas Instruments

Important

Texas Instruments makes no warranty, either expressed or implied,
including but not limited to any implied warranties of
merchantability and fitness for a particular purpose, regarding any
programs or book materials and makes such materials available
solely on an “as-is” basis.

In no event shall Texas Instruments be liable to anyone for special,
collateral, incidental, or consequential damages in connection with or
arising out of the purchase or use of these materials, and the sole and
exclusive liability of Texas Instruments, regardless of the form of
action, shall not exceed the purchase price of this equipment.
Moreover, Texas Instruments shall not be liable for any claim of any
kind whatsoever against the use of these materials by any other party.

US FCC Information
Concerning Radio
Frequency
Interference

This equipment has been tested and found to comply with the limits
for a Class B digital device, pursuant to Part 15 of the FCC rules. These
limits are designed to provide reasonable protection against harmful
interference in a residential installation. This equipment generates,
uses, and can radiate radio frequency energy and, if not installed and
used in accordance with the instructions, may cause harmful
interference with radio communications. However, there is no
guarantee that interference will not occur in a particular installation.

If this equipment does cause harmful interference to radio or
television reception, which can be determined by turning the
equipment off and on, you can try to correct the interference by one
or more of the following measures:

¦

Reorient or relocate the receiving antenna.

¦

Increase the separation between the equipment and receiver.

¦

Connect the equipment into an outlet on a circuit different from
that to which the receiver is connected.

¦

Consult the dealer or an experienced radio/television technician
for help.

Caution:

expressly approved by Texas Instruments may void your authority to
operate the equipment.

Any changes or modifications to this equipment not

ii

Table of Contents

Chapter 1:
Getting Started

Chapter 2:
Operating the
Calculator

This guidebook describes how to use the
table of contents can help you locate "getting started"
information as well as detailed information about the

TI-89 / TI-92 Plus

location to find details about every
and instruction.

Flash Applications .....................................................................................x

Keystroke Differences.............................................................................xii

What’s New? ............................................................................................xiv

Getting the TI.89 Ready to Use................................................................ 2

Getting the TI.92 Plus Ready to Use ....................................................... 3

Setting the Contrast and Selecting a Language...................................... 4

Performing Computations ........................................................................ 8

Graphing a Function................................................................................ 11

Turning the TI.89 / TI.92 Plus On and Off ............................................ 14

Setting the Display Contrast................................................................... 15

The TI.89 Keyboard................................................................................. 16

The TI.92 Plus Keyboard ........................................................................ 17

Modifier Keys............................................................................................ 18

Entering Alphabetic Characters............................................................. 21

Home Screen ............................................................................................ 23

Entering Numbers.................................................................................... 25

Entering Expressions and Instructions................................................. 26

Formats of Displayed Results ................................................................ 29

Editing an Expression in the Entry Line............................................... 32

Menus ........................................................................................................ 34

Using the Custom Menu.......................................................................... 37

Selecting an Application ......................................................................... 38

Setting Modes ........................................................................................... 40

Using the Clean Up Menu to Start a New Problem.............................. 43

Using the Catalog Dialog Box................................................................. 44

Storing and Recalling Variable Values................................................... 47

Reusing a Previous Entry or the Last Answer...................................... 49

Auto-Pasting an Entry or Answer from the History Area ................... 52

Status Line Indicators in the Display..................................................... 53

Finding the Software Version and ID Number..................................... 55

features. Appendix A provides one convenient

TI-89 / TI-92 Plus

TI-89 / TI-92 Plus

function

. The

iii

Chapter 3:
Symbolic
Manipulation

Preview of Symbolic Manipulation........................................................ 58

Using Undefined or Defined Variables.................................................. 59

Using Exact, Approximate, and Auto Modes ....................................... 61

Automatic Simplification ........................................................................ 64

Delayed Simplification for Certain Built-In Functions ....................... 66

Substituting Values and Setting Constraints ........................................67

Overview of the Algebra Menu............................................................... 70

Common Algebraic Operations.............................................................. 72

Overview of the Calc Menu..................................................................... 75

Common Calculus Operations ............................................................... 76

User-Defined Functions and Symbolic Manipulation ......................... 77

If You Get an Out-of-Memory Error....................................................... 79

Special Constants Used in Symbolic Manipulation............................. 80

Chapter 4:
Constants and
Measurement Units

Chapter 5:
Additional Home
Screen Topics

Chapter 6:
Basic Function
Graphing

Preview of Constants and Measurement Units.................................... 82

Entering Constants or Units ................................................................... 83

Converting from One Unit to Another................................................... 85

Setting the Default Units for Displayed Results................................... 87

Creating Your Own User-Defined Units................................................ 88

List of Pre-Defined Constants and Units............................................... 89

Saving the Home Screen Entries as a Text Editor Script ................... 94

Cutting, Copying, and Pasting Information ..........................................95

Creating and Evaluating User-Defined Functions ............................... 97

Using Folders to Store Independent Sets of Variables ..................... 100

If an Entry or Answer Is “Too Big” ......................................................103

Preview of Basic Function Graphing................................................... 106

Overview of Steps in Graphing Functions.......................................... 107

Setting the Graph Mode ........................................................................ 108

Defining Functions for Graphing......................................................... 109

Selecting Functions to Graph............................................................... 111

Setting the Display Style for a Function ............................................. 112

Defining the Viewing Window.............................................................. 113

Changing the Graph Format ................................................................. 114

Graphing the Selected Functions......................................................... 115

Displaying Coordinates with the Free-Moving Cursor...................... 116

Tracing a Function................................................................................. 117

Using Zooms to Explore a Graph......................................................... 119

Using Math Tools to Analyze Functions ............................................. 122

Chapter 7:
Parametric
Graphing

iv

Preview of Parametric Graphing.......................................................... 128

Overview of Steps in Graphing Parametric Equations...................... 129

Differences in Parametric and Function Graphing............................ 130

Chapter 8:
Polar Graphing

Preview of Polar Graphing.................................................................... 134

Overview of Steps in Graphing Polar Equations................................ 135

Differences in Polar and Function Graphing...................................... 136

Chapter 9:
Sequence Graphing

Chapter 10:
3D Graphing

Chapter 11:
Differential
Equation Graphing

Preview of Sequence Graphing ............................................................ 140

Overview of Steps in Graphing Sequences ......................................... 141

Differences in Sequence and Function Graphing .............................. 142

Setting Axes for Time, Web, or Custom Plots.................................... 146

Using Web Plots ..................................................................................... 147

Using Custom Plots ............................................................................... 150

Using a Sequence to Generate a Table................................................ 151

Preview of 3D Graphing........................................................................ 154

Overview of Steps in Graphing 3D Equations .................................... 156

Differences in 3D and Function Graphing.......................................... 157

Moving the Cursor in 3D ....................................................................... 160

Rotating and/or Elevating the Viewing Angle..................................... 162

Animating a 3D Graph Interactively .................................................... 164

Changing the Axes and Style Formats ................................................ 165

Contour Plots.......................................................................................... 167

Example: Contours of a Complex Modulus Surface ......................... 170

Implicit Plots .......................................................................................... 171

Example: Implicit Plot of a More Complicated Equation................. 173

Preview of Differential Equation Graphing........................................ 176

Overview of Steps in Graphing Differential Equations..................... 178

Differences in Diff Equations and Function Graphing...................... 179

Setting the Initial Conditions................................................................ 184

Defining a System for Higher-Order Equations.................................. 186

Example of a 2nd-Order Equation ....................................................... 187

Example of a 3rd-Order Equation........................................................ 189

Setting Axes for Time or Custom Plots............................................... 190

Example of Time and Custom Axes .................................................... 191

Example Comparison of RK and Euler ............................................... 193

Example of the deSolve( ) Function.................................................... 196

Troubleshooting with the Fields Graph Format ................................ 197

v

Chapter 12:
Additional
Graphing Topics

Preview of Additional Graphing Topics.............................................. 202

Collecting Data Points from a Graph .................................................. 203

Graphing a Function Defined on the Home Screen........................... 204

Graphing a Piecewise Defined Function............................................. 206

Graphing a Family of Curves................................................................ 208

Using the Two-Graph Mode.................................................................. 209

Drawing a Function or Inverse on a Graph ........................................ 212

Drawing a Line, Circle, or Text Label on a Graph ............................. 213

Saving and Opening a Picture of a Graph........................................... 217

Animating a Series of Graph Pictures ................................................. 219

Saving and Opening a Graph Database ............................................... 220

Chapter 13:
Tables

Chapter 14:
Split Screens

Chapter 15:
Data/Matrix Editor

Chapter 16:
Statistics and
Data Plots

Preview of Tables................................................................................... 222

Overview of Steps in Generating a Table............................................ 223

Setting Up the Table Parameters ......................................................... 224

Displaying an Automatic Table ............................................................ 226

Building a Manual (Ask) Table............................................................. 229

Preview of Split Screens ....................................................................... 232

Setting and Exiting the Split Screen Mode ......................................... 233

Selecting the Active Application.......................................................... 235

Preview of the Data/Matrix Editor....................................................... 238

Overview of List, Data, and Matrix Variables..................................... 239

Starting a Data/Matrix Editor Session................................................. 241

Entering and Viewing Cell Values........................................................ 243

Inserting and Deleting a Row, Column, or Cell.................................. 246

Defining a Column Header with an Expression................................. 248

Using Shift and CumSum Functions in a Column Header................ 250

Sorting Columns..................................................................................... 251

Saving a Copy of a List, Data, or Matrix Variable .............................. 252

Preview of Statistics and Data Plots.................................................... 254

Overview of Steps in Statistical Analysis............................................ 258

Performing a Statistical Calculation.................................................... 259

Statistical Calculation Types................................................................ 261

Statistical Variables ............................................................................... 263

Defining a Statistical Plot...................................................................... 264

Statistical Plot Types............................................................................. 266

Using the Y= Editor with Stat Plots..................................................... 268

Graphing and Tracing a Defined Stat Plot.......................................... 269

Using Frequencies and Categories ...................................................... 270

If You Have a CBL or CBR .................................................................... 272

vi

Chapter 17:
Programming

Preview of Programming ...................................................................... 276

Running an Existing Program .............................................................. 278

Starting a Program Editor Session....................................................... 280

Overview of Entering a Program ......................................................... 282

Overview of Entering a Function......................................................... 285

Calling One Program from Another..................................................... 287

Using Variables in a Program ............................................................... 288

Using Local Variables in Functions or Programs................................... 290

String Operations ................................................................................... 292

Conditional Tests ................................................................................... 294

Using If, Lbl, and Goto to Control Program Flow.............................. 295

Using Loops to Repeat a Group of Commands.................................. 297

Configuring the TI-89 / TI-92 Plus ....................................................... 300

Getting Input from the User and Displaying Output .........................301

Creating a Custom Menu....................................................................... 303

Creating a Table or Graph..................................................................... 305

Drawing on the Graph Screen .............................................................. 307

Accessing Another TI.89 / TI.92 Plus, a CBL, or a CBR.................... 309

Debugging Programs and Handling Errors......................................... 310

Example: Using Alternative Approaches ............................................ 311

Assembly-Language Programs ............................................................. 313

Chapter 18:
Text Editor

Chapter 19:
Numeric Solver

Chapter 20:
Number Bases

Preview of Text Operations.................................................................. 316

Starting a Text Editor Session.............................................................. 317

Entering and Editing Text..................................................................... 319

Entering Special Characters.................................................................. 324

Entering and Executing a Command Script....................................... 328

Creating a Lab Report............................................................................ 330

Preview of the Numeric Solver ............................................................ 334

Displaying the Solver and Entering an Equation ............................... 335

Defining the Known Variables.............................................................. 337

Solving for the Unknown Variable....................................................... 339

Graphing the Solution ........................................................................... 340

Preview of Number Bases..................................................................... 344

Entering and Converting Number Bases............................................. 345

Performing Math Operations with Hex or Bin Numbers .................. 346

Comparing or Manipulating Bits.......................................................... 347

vii

Chapter 21:
Memory and
Variable
Management

Preview of Memory and Variable Management ................................. 350

Checking and Resetting Memory ......................................................... 353

Displaying the VAR-LINK Screen......................................................... 355

Manipulating Variables and Folders with VAR-LINK ........................ 357

Pasting a Variable Name to an Application ........................................ 359

Archiving and Unarchiving a Variable................................................. 360

If a Garbage Collection Message Is Displayed ................................... 362

Memory Error When Accessing an Archived Variable...................... 364

Chapter 22:
Linking and
Upgrading

Chapter 23:
Activities

Linking Two Units.................................................................................. 366

Transmitting Variables, Flash Applications, and Folders................. 367

Transmitting Variables under Program Control................................. 371

Upgrading Product Software (Base Code) ......................................... 373

Collecting and Transmitting ID Lists................................................... 378

Compatibility between a TI.89, TI.92 Plus, and TI.92 ...................... 380

Analyzing the Pole-Corner Problem .................................................... 384

Deriving the Quadratic Formula .......................................................... 386

Exploring a Matrix................................................................................. 388

Exploring cos(x) = sin(x) ..................................................................... 389

Finding Minimum Surface Area of a Parallelepiped.......................... 390

Running a Tutorial Script Using the Text Editor............................... 392

Decomposing a Rational Function ...................................................... 394

Studying Statistics: Filtering Data by Categories............................... 396

CBL Program for the TI-89 / TI-92 Plus .............................................. 399

Studying the Flight of a Hit Baseball................................................... 400

Visualizing Complex Zeros of a Cubic Polynomial ............................. 402

Solving a Standard Annuity Problem................................................... 404

Computing the Time-Value-of-Money.................................................. 405

Finding Rational, Real, and Complex Factors.................................... 406

Simulation of Sampling without Replacement................................... 407

Appendix A:
Functions and
Instructions

viii

Quick-Find Locator................................................................................ 410

Alphabetical Listing of Operations ...................................................... 414

Appendix B:
Reference
Information

TI-89 / TI-92 Plus Error Messages ....................................................... 542

Modes ...................................................................................................... 550

TI-89 / TI-92 Plus Character Codes ..................................................... 555

TI.89 Key Codes ..................................................................................... 556

TI.92 Plus Key Codes............................................................................. 559

Entering Complex Numbers ................................................................. 563

Accuracy Information............................................................................ 566

System Variables and Reserved Names .............................................. 567

EOS (Equation Operating System) Hierarchy.................................... 568

Regression Formulas............................................................................. 570

Contour Levels and Implicit Plot Algorithm....................................... 572

Runge-Kutta Method.............................................................................. 573

Appendix C:
Service and
Warranty
Information

Appendix D:
Programmer’s
Guide

Battery Information ............................................................................... 576

In Case of Difficulty............................................................................... 579

Support and Service Information......................................................... 580

Warranty Information............................................................................ 581

setMode( ) and getMode( ) ................................................................... 584

setGraph( ).............................................................................................. 587

setTable( )............................................................................................... 589

Index........................................................................................................ 591

TI-89 Shortcut Keys ...................................................... inside front cover

TI-92 Plus Shortcut Keys ..............................................inside back cover

ix

Flash Applications

y

g

Applications

Hardware/Software
Requirements

Hardware Setup for
the Computer

Flash functionality enables the ability to download different
applications to a

TI-89 / TI-92 Plus

calculator from the enclosed

CD-ROM, the TI web site, or from another calculator.

Before downloading new applications to a

TI-89 / TI-92 Plus

read and accept the license agreement on the

TI-89 / TI-92 Plus

, please

Applications CD-ROM.

Before installing Flash applications, you will need:

• A computer with a CD-ROM drive and a serial port.

•

TI-GRAPH LINK

, available separately as software and a cable

é

that connects your computer and calculator.
If you need
site at:

http://www.ti.com/calc/docs/link.htm

TI-GRAPH LINK

software or a cable, check the TI web

To set up:

1. Insert the small end of the
the bottom of the

or the top of the

TI-89

TI-GRAPH LINK

cable into the port at

TI-92 Plus

.

2. Connect the other end to the computer’s serial port using a
25-to-9 pin adapter if necessary.

Installing a Flash
Application from the
CD-ROM

Note: For further

information about
transmitting to and from

our computer, refer to the

TI-GRAPH LINK

uidebook.

Running a Flash
Application

To install an application:

1. Insert the

TI-89 / TI-92 Plus

Applications CD-ROM into the

computer’s CD-ROM drive.

2. From the computer, start the

3. From the

Certificates

menu, click

Link

.

Send Flash Software 8 Applications and

TI-GRAPH LINK

software.

4. Locate the Flash application on the CD-ROM and double-click.
The Flash application is copied to the calculator.

To run an application:

1. On the

APPLICATIONS

TI-89 / TI-92 Plus

menu.

, press ¥ O to display the

FLASH

2. Use the cursor keys CD to highlight the application and press
¸.

x

Transferring a Flash

y

g

Application from
another
TI-89 / TI-92 Plus

This guidebook uses

Note:

screen shots.

TI-89

Do not attempt to transfer an application if a low-battery message
appears on either the receiving or sending calculator.

1. Connect the calculators with the calculator-to-calculator cable
that came with the

TI-89 / TI-92 Plus

.

2. On the sending calculator:

a. Press 



b. Press:



h

‰

TI-89:
TI-92 Plus:

c. Highlight the Flash application and press † (a Ÿ is displayed

to the left of the selected item)

3. On the receiving calculator:

a. Press 
b. Press
c. Select:
d. Press



…

2:Receive

¸

4. On the sending calculator:

a. Press
b. Select:
c. Press

…

1:Send to TI-89/92 Plus

¸

Backing up a Flash
Application

For further

Note:

information about
transmitting to and from

our computer, refer to the

TI-GRAPH LINK

uidebook

.

Deleting a Flash
Application

To select all Flash

Note:

applications, use the
menu.

f

To back up an application to the computer:

1. On the calculator, press:



TI-89:
TI-92 Plus:

2. From the computer, start the

3. From the

"

¹

menu, click

Link

TI-GRAPH LINK

Receive Flash Software

software

4. Select one or more Flash applications and click add

5. Click ok

6. Save the application to the computer and record this information
for future reference.

To delete a Flash application from the calculator:

1. Press 



to display the

VAR-LINK

screen

2. Press:



h

‰

TI-89:
TI-92 Plus:

3. Highlight the Flash application and press † (a Ÿis displayed to

All

the left of the selected item)

4. Press ƒ and choose

1:Delete

— or —
Press 0 (a confirmation message appears)

5. Press

¸

to confirm the deletion.

xi

Keystroke Differences

There are certain differences in keystrokes using the

TI-89 / TI-92 Plus

for various operations. The

following table shows the keystrokes for major commands for the two calculators.

³

FUNCTION
LETTERS

One lowercase letter (a-s, u, v, w)
One lowercase letter (t, x, y, z)
Several lowercase letters
End several lowercase letters
Several uppercase letters
End several uppercase letters

FUNCTION KEYS

F6
F7
F8

NAVIGATION

Scroll tall objects up or down in history

j

T, X, Y, Z T, X, Y, Z

2 ™

j

¤ ™ 2 ¢

j 2 ¢

2 ˆ ˆ

2 ‰ ‰

2 Š Š

¤ C, ¤ D ‚ C, ‚ D

TI-89

A-S, U-W A-S, U-W

›

TI-92 Plus

.

Move cursor far left or far right on entry line
Diagonal movement

FUNCTIONS

Display Home screen
Cut
Copy
Paste
Catalog
Display Units dialog box
Sin
Cos
Tan
LN

õ¥

e
EE

2 A, 2 B2

C
C
D
D

and
and
and
and

A
B
A
B

A, 2

E F G H

" ¥ "

¥ 5 ¥

¥ 6 ¥

¥ 7 ¥

X
C
V

½ 2 ½

2 9 ¥ 9

2 W W

2 X X

2 Y Y

2 x x

s 2 s

^ 2 ^

B

xii

FUNCTION
SYMBOLS

ú

(Conversion triangle)

³

TI-89

2  2 

›

TI-92 Plus

_ (Underscore)

θ

(Theta)
| (“With”)
' (Prime)

°

(Degree)

∠

(Angle)

Σ

(Sigma)
xê (Reciprocal)
Space

HIDDEN SHORTCUTS

Place data in sysdata variable
Greek characters
Keyboard map
Place data in Home screen history
Grave (à, è, ì, ò, ù)
Cedilla (ç)

¥  2 

¥ Ï Ï

Í 2 Í

2 È 2 È

2 v 2 v

2 ’ 2 ’

½

½

Σ (
^-1

j

¥ b ¥

¥ c j

or ¥ c

¤ ¥

2 >

2 V

Space bar

D

G or

¥ ^ ¥ ”

¥ · ¥

2 ¿

2 ¿

5
5 6

H

2

A a, e, i, o, u

2

C c

¥

G

¤

Acute (á, é, í, ó, ú, ý)
Tilde (ã, ñ, õ)
Caret (â, ê, î, ô, û)
Umlaut (ä, ë, ï, ö, ü, ÿ)
? (Question mark)

β

(Beta)
# (Indirection)
& (Append)
@ (Arbitrary)

≠

(Not equal to symbol)
! (Factorial)
Comment (Circle-C)
New
Open
Save copy as
Format dialog box

2 ¿

2 ¿

2 ¿

2 ¿

2 ¿

2 ¿

2 ¿

¥ p

(times)

5
5 6
5
5
3
5 6
3

2

2

2

2

2

2

2

2

¥ § 2

¥ Á 2

¥ e 2

¥ d

ƒ

ƒ

ƒ

¦ 2

3
1
2

¥

¥

¥

¥ Í ¥

E a, e, i, o, u, y
N a, n, o
O a, e, i, o, u
U a, e, i, o, u, y
Q
S
T
H
R
V
W

¦

X
N
O
S
F

xiii

What’s New?

Introducing
Advanced
Mathematics
Software
Version 2.0

TI developed the Advanced Mathematics
Software Version 2.0 to enable
downloadable calculator software
applications for the

Advanced Mathematics Software Version 2.0 is an infrastructure
enhancement of the current Advanced Mathematics Software
Version 1.xx. It has all the features of Version 1.xx. The improved
infrastructure enables multiple downloadable calculator software
applications, language localization. This enhancement also provides
your new
over 702-KB Flash memory between user data archive and calculator
software applications.

All previous

2.0. However, on some
data archive can only occupy a maximum of 384-KB of the over
702-KB Flash memory shared with calculator software applications.

You can download Advanced Mathematics Software Version 2.0 to
your computer from the TI web site at
then transfer it to your
software and the computer-calculator cable (available separately).
You can also transfer the software from one
another using the unit-to-unit cable. The Advanced Mathematics
Software is free from the TI web site at

TI-89 / TI-92 Plus

and

TI-89

and

TI-89

TI-92 Plus Modules

TI-89

TI-92 Plus

with maximum reapportionment of the

and all

TI-89 / TI-92 Plus

.

can be upgraded to Version

TI-92 Plus Module

http://www.ti.com/calc/flash

using the

http://www.ti.com/calc/flash

For details, refer to:

Chapter 21 and 22

units, the user

TI.GRAPH LINK

TI-89 / TI-92 Plus

,

é

to

Language
Localization

Improved User
Interface

The

TI-89 / TI-92 Plus

other languages. These free applications
translate prompts, error messages, and
most functions into one of several
languages.

The improved user interface allows folder collapse/expand and
expands the
user-defined functions.

CATALOG

can be localized into

menu to include application functions and

For details, refer to:

Chapter 1

xiv

v
A

p
p

Upgradability with
Flash ROM

The

TI-89 / TI-92 Plus

which lets you upgrade future software

ersions without buying a new calculator.

uses Flash technology,

For details, refer to:

Chapter 22

s new functionality becomes available, you can electronically

upgrade your

TI-89 / TI-92 Plus

. Future software versions include
maintenance upgrades that will be released free of charge, as well as
new applications and major future upgrades that will be available for

urchase from the TI web site.

To download upgrades from the TI web site, you must have an
Internet-connected computer,

TI.GRAPH LINK

software and the

é

computer-to-calculator cable (available separately). You can also
transfer the product software (base code) and Flash applications
from one

TI-89 / TI-92 Plus

to another using a unit-to-unit cable,

rovided that the receiving calculator is also licensed to run that

software.

Custom Menu

New to the

TI-92 Plus

is the custom menu feature that lets you create
your own toolbar menu. A custom menu can contain any available
function, instruction, or set of characters. The

TI-92 Plus

has a default

custom menu that you can modify or redefine.

xv

Chapter 1:
Getting Started

Getting the TI.89 Ready to Use ................................................................ 2

Getting the TI.92 Plus Ready to Use ....................................................... 3

Setting the Contrast and Selecting a Language...................................... 4

Performing Computations ........................................................................ 8

Graphing a Function................................................................................ 11

1

This chapter helps you to get started using the
quickly. This chapter takes you through several examples to
introduce you to some of the principal operating and graphing
functions of the

After setting up your
examples, please read Chapter 2: Operating the Calculator. You
then will be prepared to advance to the detailed information
provided in the remaining chapters in this guidebook.

TI-89 / TI-92 Plus

TI-89 / TI-92 Plus

.

and completing these

TI-89 / TI-92 Plus

Chapter 1: Getting Started 1

Getting the TI.89 Ready to Use

Installing the AAA
Batteries

Important:

batteries in the future,
ensure that the
turned off by pressing

2®

When replacing

TI-89

.

is

The

comes with four AAA batteries. This chapter

TI-89

describes how to install these batteries. It also describes how
to turn the unit on for the first time, set the display contrast,
select a language, and view the Home screen for both the

and the

TI-89

TI-92 Plus.

To install the four AAA batteries:

1. Place the

face down on a soft cloth to prevent scratching the

TI-89

display face.

2. On the back of the calculator, depress the battery cover latch. Lift

and remove the battery cover.

3. Remove the batteries from the package and install them in the

battery compartment. Arrange the batteries according to the
polarity (+ and N) diagram in the battery compartment.

4. Replace the battery cover by inserting the two prongs into the

two slots at the bottom of the battery compartment, and then
push the cover until the latch snaps closed.

To replace the batteries without losing any information stored in
memory, follow the directions in Appendix C.

2 Chapter 1: Getting Started

Lithium battery

AAA batteries

Getting the TI.92 Plus Ready to Use

Installing the AA
Batteries

Important:

batteries in the future,
ensure that the
turned off by pressing

2 ®

When replacing

TI-92 Plus

.

The

TI-92 Plus

comes with four AA batteries. This chapter
describes how to install these batteries. It also describes how
to turn the unit on for the first time, set the display contrast,
select a language, and view the Home screen for both the

TI-92 Plus

and the

TI-89.

To install the four AA alkaline batteries:

1. Holding the

TI-92 Plus

unit upright, slide the latch on the top of
the unit to the left unlocked position; slide the rear cover down
about one-eighth inch and remove it from the main unit.

Slide to open.

is

2. Place the

TI-92 Plus

face down on a soft cloth to prevent

scratching the display face.

3. Install the four AA batteries. Be sure to position the batteries
according to the diagram inside the unit. The positive (+) terminal
of each battery should point toward the top of the unit.

top

I/O

back

AA batteries

Lithium battery

4. Replace the rear cover and slide the latch on the top of the unit to
the right locked position to lock the cover back in place.

Chapter 1: Getting Started 3

Setting the Contrast and Selecting a Language

Turning the Unit on
and Adjusting the
Display Contrast

Languages on the
TI

89 / TI.92 Plus

.

After you install the batteries in your
possible that the display contrast may be too dark or too dim to see
anything.

To adjust the display to your satisfaction, hold down ¥(diamond
symbol inside a green border) and momentarily press |(minus key)
to lighten the display. Hold down ¥and momentarily press «(plus
key) to darken the display.

You will see a screen that lists several languages. The list of
languages on your calculator may vary from this example.

Languages other than English are available as Flash applications.
English is part of the product software (base code). You may keep as
many or as few alternate languages on your calculator as you want
(subject to memory limitation) and switch between them easily.
During the process, you will be given an opportunity to choose
additional languages to keep or delete. You may also add or delete
language applications through the

TI-89 / TI-92 Plus

VAR-LINK

screen.

, press ´. It is

Important Information
About the Language
Process

The
Localizing means that all menu names, dialog boxes, error messages,
etc., will display in the language of your choice.

The
time; however, you can keep additional languages on the unit and
switch the language at any time.

The initial localization of the

¦

¦

English cannot be

Note:

deleted and remains
available in the product
software (base code).

4 Chapter 1: Getting Started

¦

TI-89 / TI-92 Plus

TI-89 / TI-92 Plus

Phase I - Select the language in which you would like to localize

TI-89 / TI-92 Plus

the
selected language.

Phase II - Read the instructional message that appears in the
language you selected in Phase I.

Phase III - The
selected in Phase I. You can now select one or more language
applications that you would like to keep on the calculator (in case
you want to switch to another language later). You can always
reload one or more language applications later, if necessary. The
calculator will then automatically delete the unselected
languages.

can be localized into one of several languages.

can be localized into only one language at a

TI-89 / TI-92 Plus

. Future online instructions will appear in the

TI-89 / TI-92 Plus

is localized into the language you

occurs in three phases:

Localizing the
TI.89 / TI.92 Plus

1. Press the cursor keys (D or C) to
move the pointer to the language in
which you would like to set your

TI-89 / TI-92 Plus

. (The list of
languages on your calculator may
vary from this example.)

Note: Until you complete
the localization process, the
Select a Language dialog
box will reappear when you
turn the unit on.

2. Press ¸ to set the

TI-89 / TI-92 Plus

into the selected language.

(Pressing N halts the localization process and displays the
Home screen.)

3. Read the message that appears and

then press ¸.

The message displays in the
language you previously selected.

4. Press the cursor keys (D or C) to move the pointer and then
press ƒ to select each additional language that you would like to
keep.
— or —
Press „ to select and keep all of the language applications.

You cannot uncheck English or the
language you selected in step 1.

Pressing ƒ toggles the Ÿ on and off.

5. Press ¸ to complete the localization process. Additional
selected languages, if any, are retained in memory and unselected
languages are deleted to free up Flash memory. (Pressing N
halts the localization process and displays the Home screen.)

If additional language applications remain on your
you can change the localization language via

Page 3

TI-89 / TI-92 Plus

(…) of the

,

Mode

dialog box. See “Setting Modes” in Chapter 2 for information on how
to use the
Flash applications via the

dialog box. You can add or delete language and other

Mode

VAR-LINK

screen. See “Transmitting

Variables, Flash Applications, and Folders” in Chapter 22.

Language applications are available on the enclosed CD and from the
Texas Instruments web site. For up-to-date information about Flash
applications, including additional language applications, check the
Texas Instruments web site at:

http://www.ti.com/calc

Chapter 1: Getting Started 5

About the Home
Screen

History Area

Lists entry/answer pairs
you have entered. Pairs
scroll up the screen as
you make new entries.

After you select a language, a blank Home screen is displayed.

The Home screen lets you execute instructions, evaluate
expressions, and view results.

The following example contains previously entered data and
describes the main parts of the Home screen. Entry/answer pairs in
the history area are displayed in “pretty print.” Pretty print displays
expressions in the same form in which they are written on the board
or in textbooks.

Toolbar

Lets you display menus for
selecting operations
applicable to the Home
screen. To display a toolbar
menu, press ƒ, „, etc.

Last Entry

Your last entry.

Entry Line

Where you enter
expressions or
instructions.

Last Answer

Result of your last entry.
Note that results are not
displayed on the entry line.

Status Line

Shows the current state of
the calculator.

6 Chapter 1: Getting Started

The following example shows an answer that is not on the same line
as the expression. Note that the answer is longer than the screen
width. An arrow (8) indicates the answer is continued. The entry line
contains ellipsis (…). Ellipsis indicates the entry is longer than the
screen width.

Last Entry

"Pretty print" is ON.
Exponents, roots,
fractions, etc., are
displayed in the same
form in which they are
traditionally written.

Answer Continues

Highlight the answer and
press B to scroll right and
view the rest of it. Note that
the answer is not on the
same line as the
expression.

Expression Continues

Press B to scroll right and
view the rest of the entry.
Press 2 A or 2 B to go
to the beginning or end of
the entry line.

Turning the
TI.89 / TI.92 Plus
Off

When you want to turn the

TI-89 / TI-92 Plus

off, press

(Note: ® is the second function of the ´ key.)

2®

.

Chapter 1: Getting Started 7

Performing Computations

This section provides several examples for you to perform that demonstrate some of the
computational features of the

TI-89 / TI-92 Plus.

cleared by pressing ƒand selecting 8:Clear Home, before performing each example, to
illustrate only the results of the example’s keystrokes.

The history area in each screen was

Steps

Showing Computations

1. Compute

and display the

sin(p/4)

result in symbolic and numeric
format.

To clear the history area of previous

calculations, press

8:Clear Home.

ƒ

and select

Finding the Factorial of Numbers

1. Compute the factorial of several
numbers to see how the

TI-89 / TI-92 Plus

handles very

large integers.

To get the factorial operator (!), press

2I

then select

, select

.

1:!

7:Probability

, and

Expanding Complex Numbers

1. Compute

TI-89 / TI-92 Plus

3

to see how the

(3+5i)

handles
computations involving complex
numbers.

³

TI.89

Keystrokes

2W2T
e4d¸
¥¸

5

2I

¸

20

2I

¸

30

2I

¸

c3«52)
dZ3¸

71

71

71

›

TI.92 Plus

Keystrokes Display

W2T
e4d¸
¥¸

¸

52W

202W

302W

c3«52)
dZ3¸

¸

¸

Finding Prime Factors

1. Compute the factors of the
rational number

You can enter “factor” on the entry line

by typing
by pressing

Optional

2. (

FACTOR

2634492

on the keyboard, or

„

and selecting

) Enter other numbers

.

2:factor(

on your own.

8 Chapter 1: Getting Started

2

„

2634492

¸

.

d

„

2

2634492

¸

d

Steps

Expanding Expressions

1. Expand the expression

You can enter “expand” on the entry

line by typing
keyboard, or by pressing
selecting

Optional

2. (

EXPAND

3:expand(

) Enter other

on the

c

.

(xË5)

and

3

.

expressions on your own.

Reducing Expressions

1. Reduce the expression

2

(x

Ë2xË

5)/(xË1)

to its simplest

form.

You can enter “propFrac” on the entry

line by typing
keyboard, or by pressing
selecting

PROPFRAC

7:propFrac(.

on the

and

c

Factoring Polynomials

2

1. Factor the polynomial

Ë

5)

(x

with respect to x.

You can enter “factor” on the entry line

by typing
by pressing

FACTOR

on the keyboard or

and selecting

c

2:factor(

TI.89

Keystrokes

3

c
CX\5D:
D


7

c
CX:2\
\5DE
CX\1DD


2

c

X:2\5

BXD


.

³

›

TI.92 Plus

Keystrokes Display

„

3

cX|5dZ

3

3

d
¸

„

7

cXZ2|

2X

2X

|5de
cX|1dd
¸

„

2

XZ2|5

bXd
¸

Solving Equations

2

1. Solve the equation

x

Ë2xË

6=2

with respect to x.

You can enter “solve(” on the entry

line by selecting
Catalog menu, by typing
the keyboard, or by pressing
selecting

The status line area shows the

required syntax for the marked item
in the Catalog menu.

1:solve(

“solve(”

.

from the

SOLVE(

c

and

„

X:2\2X\6

2BXD


on

„

1

1

XZ2|2X|6

Á2bXd
¸

Chapter 1: Getting Started 9

Steps

Í

s

Solving Equations with a Domain
Constraint

2

1. Solve the equation

x

ì2xì

6=2

with respect to x where x is
greater than zero.

The “with” (I) operator provides

domain constraint.

Í

TI.89:
TI.92 Plus:

2

Finding the Derivative of
Functions

1. Find the derivative of

2

(xìy)3/(x+y)

This example illustrates using the

calculus differentiation function and
how the function is displayed in “pretty
print” in the history area.

with respect to x.

Finding the Integral of Function

³

TI.89

Keystrokes

„

1

XZ2|2X|6

Á2bXd

X

Í

0

2Ã
¸

2=cX|

Y

dZ3ecX«

Y

dZ2bXd

¸

›

TI.92 Plus

Keystrokes Display

„

1

XZ2|2X|6

Á2bXd
2 Í

X

2Ã

0

¸

2=cX|

Y

dZ3ecX«

dZ2bXd

Y

¸

1. Find the integral of
respect to

This example illustrates using the

calculus integration function.

.

x

xùsin(x)

with

2<Xp
2WXdb

X

d¸

2<Xp
WXdb

d¸

X

10 Chapter 1: Getting Started

Graphing a Function

The example in this section demonstrates some of the graphing capabilities of the

TI-89 / TI-92 Plus

how to enter a function, produce a graph of the function, trace a curve, find a minimum
point, and transfer the minimum coordinates to the Home screen.

. It illustrates how to graph a function using the Y= Editor. You will learn

Explore the graphing capabilities of the

2

y=(|x

ì3|ì

10)/2

.

Steps

1. Display the Y= Editor.

2. Enter the function

2

(abs(x

ì3)ì

10)/2

.

3. Display the graph of the
function.

Select

6:ZoomStd

moving the cursor to
pressing

¸

by pressing 6 or by

6:ZoomStd

.

and

TI-89 / TI-92 Plus

³

TI.89

Keystrokes

¥#

c½
¸

XZ2|3
10

de

d|

2

¸

6

„

A

by graphing the function

›

TI.92 Plus

Keystrokes Display

¥#

c2½

¸

XZ2|3

de

10

¸

„

6

A

d|

2

entry line

“pretty print”
display of the
function in the
entry line

4. Turn on Trace.

The tracing cursor, and the x and y

coordinates are displayed.

5.

Open the

3:Minimum

menu and select

MATH

.

…

‡DD¸

…

tracing
cursor

‡DD¸

Chapter 1: Getting Started 11

Steps

6. Set the lower bound.

Press B(right cursor) to move the

tracing cursor until the lower bound for
x is just to the left of the minimum
node before pressing
second time.

¸

the

7. Set the upper bound.

Press B(right cursor) to move the

tracing cursor until the upper bound for
x is just to the right of the minimum
node.

³

TI.89

Keystrokes

B

B

...

¸

B

B

...

›

TI.92 Plus

Keystrokes Display

B

B

...

¸

B

B

...

8. Find the minimum point on the
graph between the lower and
upper bounds.

9. Transfer the result to the Home
screen, and then display the
Home screen.

Shortcuts for copying graph

coordinates to Home screen history:

¥·

TI.89:
TI.92 Plus:

¥

H

¸

¥·
"

¸

¥

H

¥"

minimum coordinates

minimum point

12 Chapter 1: Getting Started

Chapter 2:
Operating the Calculator

Turning the TI.89 / TI.92 Plus On and Off ............................................ 14

Setting the Display Contrast................................................................... 15

The TI.89 Keyboard................................................................................. 16

The TI.92 Plus Keyboard ........................................................................ 17

2

Modifier Keys............................................................................................ 18

Entering Alphabetic Characters............................................................. 21

Home Screen ............................................................................................ 23

Entering Numbers.................................................................................... 25

Entering Expressions and Instructions................................................. 26

Formats of Displayed Results ................................................................ 29

Editing an Expression in the Entry Line............................................... 32

Menus ........................................................................................................ 34

Using the Custom Menu.......................................................................... 37

Selecting an Application ......................................................................... 38

Setting Modes ........................................................................................... 40

Using the Clean Up Menu to Start a New Problem.............................. 43

Using the Catalog Dialog Box................................................................. 44

Storing and Recalling Variable Values................................................... 47

Reusing a Previous Entry or the Last Answer...................................... 49

Auto-Pasting an Entry or Answer from the History Area ................... 52

Status Line Indicators in the Display..................................................... 53

Finding the Software Version and ID Number..................................... 55

This chapter gives a general overview of the
describes its basic operations. By becoming familiar with the
information in this chapter, you can use the
solve problems more effectively.

The Home screen is the most commonly used application on the

TI-89 / TI-92 Plus

variety of mathematical operations.

. You can use the Home screen to perform a wide

TI-89 / TI-92 Plus

TI-89 / TI-92 Plus

and

to

Chapter 2: Operating the Calculator 13

p

p

Turning the TI.89 / TI.92 Plus On and Off

Turning the
TI.89 / TI.92 Plus
On

Turning the
TI.89 / TI.92 Plus Off

is the second

Note:

®

function of the ´key.

You can turn the
the ´and
the APDé (Automatic Power Downé) feature lets the

TI-89 / TI-92 Plus

Press ´.

¦

If you turned the unit off by pressing
returns to the Home screen.

¦

If you turned the unit off by pressing
itself off through APD, the
application you used last.

You can use either of the following keys to turn off the

Press: Description

2®

(press
and then

2

ress ®)

TI-89 / TI-92 Plus

2®

turn itself off automatically.

Settings and memory contents are retained by the
Constant Memoryé feature. However:

¦

¦

¥®

(or

You cannot use
displayed.

When you turn the
always displays the Home screen (regardless of
the last application you used).

on and off manually by using

) keys. To prolong battery life,

2®

¥®

TI-89 / TI-92 Plus

2®

TI-89 / TI-92 Plus

, the

or if the unit turned

returns to whichever

if an error message is

TI-89 / TI-92 Plus

TI-89 / TI-92 Plus

on again, it

.

APD (Automatic
Power Down)

Batteries

¥®

(press
and then

After several minutes without any activity, the
itself off automatically. This feature is called APD.

When you press ´, the

¦

¦

APD does not occur if a calculation or program is in progress, unless
the program is paused.

The
battery. The
back-up lithium battery. To replace the batteries in either calculator
without losing any information stored in memory, follow the
directions in Appendix C.

¥

ress ®)

The display, cursor, and any error conditions are exactly as you
left them.

All settings and memory contents are retained.

uses four AAA alkaline batteries and a back-up lithium

TI-89

Similar to

¦

You can use
displayed.

¦

When you turn the
will be exactly as you left it.

TI-92 Plus

2®

TI-89 / TI-92 Plus

uses four AA alkaline batteries and also has a

except:

¥®

if an error message is

TI-89 / TI-92 Plus

will be exactly as you left it.

on again, it

TI-89 / TI-92 Plus

turns

14 Chapter 2: Operating the Calculator

Setting the Display Contrast

The brightness and contrast of the display depend on room
lighting, battery freshness, viewing angle, and the adjustment
of the display contrast. The contrast setting is retained in
memory when the

TI-89 / TI-92 Plus

is turned off.

Adjusting the
Display Contrast

When to Replace
Batteries

The display may be

Tip:

very dark after you change
batteries. Use
lighten the display.

¥|

to

You can adjust the display contrast to suit your viewing angle and
lighting conditions.

To: Press and hold both:

Decrease (lighten) the contrast
Increase (darken) the contrast

contrast keys

TI-89

VAR-LINK O

CHAR U

If you press and hold

¥|

or

¥

¥

TI-92 Plus

¥«

contrast keys

VAR-LINK

CHAR

too long, the display may go

and
and

|

«

completely black or blank. To make finer adjustments, hold ¥and
then tap |or «.

As the batteries get low, the display begins to dim (especially during
calculations) and you must increase the contrast. If you have to
increase the contrast frequently, replace the four alkaline batteries.

The status line along the bottom of the display also gives battery
information.

Indicator in status line Description

Batteries are low.

Using the TI.92 Plus
Cover as a Stand

Slide the tabs at the

Note:

top-sides of the
into the slots in the cover.

TI-92 Plus

Replace batteries as soon as possible.

When using the

TI-92 Plus

on a desk or table top, you can use the
snap-on cover to prop up the unit at one of three angles. This may
make it easier to view the display under various lighting conditions.

Chapter 2: Operating the Calculator 15

The TI.89 Keyboard

A

Overview of Some
Important Keys

through 2

ƒ

function keys let you

select toolbar menus.

Used with ¥, you can

also select applications

Š

(page 39).

Use this section to familiarize yourself with the various keys on
the

keyboard. Most keys can perform two or more

TI-89

functions, depending on whether you first press a modifier key.

N

cancels a menu or

dialog box.

2, ¥, ¤

modify the action of

other keys (page 18).

displays the Home

"

screen, where you

X, Y, and Z are often

lets you view and

3

change

determine how numbers

and graphs are interpreted,

calculated, and displayed

, and

perform most

calculations.

used in symbolic

calculations.

mode settings that

(page 40).

Moving the Cursor

j

¸

e

executes an instruction, selects a
menu item, etc.

You can use

approximate numerical result.

, B, C, and D move

the cursor.

lets you select an

O

application (page 38).

erases the entry line.

M

Also used to delete an
entry/answer pair in the
history area.

lets you select

½

from a list of functions
and instructions (page 44).

Adjust the contrast by
pressing ¥ | (lighten) or

¥ «

(darken).

valuates an expression,

¥ ¸

To move the cursor in a particular direction, press the appropriate
cursor key (A, B, C, or D).

to display an

Some

2 A

¦

2 C

¦

¥ C

¦

C

¦

applications also let you press:

TI-89

or 2 B to move to the beginning or end of a line.

or 2 D to move up or down one screen at a time.

or ¥ D to move to the top or bottom of a page.

and A, C and B, D and A, or D and B to move diagonally.

(Press the indicated cursor keys simultaneously.)

16 Chapter 2: Operating the Calculator

The TI.92 Plus Keyboard

j

Keyboard Areas

Function Keys

Access the toolbar menus
displayed across the top
of the screen.

Application
Shortcut Keys

Used with the
key to let you
select commonly
used
applications.

¥

HOME Y= WINDOW GRAPH TblSet TABLE

With the

TI-92 Plus’s

easy-to-hold shape and keyboard layout,
you can quickly access any area of the keyboard even when
you are holding the unit with two hands.

The keyboard is divided into several areas of related keys.

Cursor Pad

Moves the display
cursor in up to 8
directions, depending
on the application.

TI-92 Plus

Cursor Pad

QWERTY Keyboard

Enters text characters

ust as you would on a

typewriter.

To move the cursor, press the applicable edge of the cursor pad. This

Calculator Keypad

Performs a variety of
math and scientific
operations.

guidebook uses key symbols such as A and B to indicate which
side of the cursor pad to press.

C

For example, press B to move the
cursor to the right.

The diagonal directions

Note:

A

B

(H, etc.) are used only for geometry
and graphing applications.

D

Chapter 2: Operating the Calculator 17

A

A

Modifier Keys

Modifier Keys

For information about

Note:

using
“Entering Alphabetic
Characters” on page 21.

Examples of

and j, refer to

¤

2

and ¥ Modifiers

Modifier Description

2

(second)

ccesses the second function of the next key you
press. On the keyboard, these are printed in the
same color as the 2 key.

¥

(diamond)

ctivates keys that select certain applications
(page 39), menu items, and other operations from
the keyboard. On the keyboard, these are printed in
the same color as the ¥ key.

¤

(shift)

Types an uppercase character for the next letter
key you press. ¤is also used with Band Ato
highlight characters in the entry line for editing
purposes.

j

(TI-89 only)

‚

(hand)

(TI-92 Plus only)

Used to type alphabetic letters, including a space
character. On the keyboard, these are printed in
the same color as the

j

key.

Used with the cursor pad to manipulate geometric
objects. ‚ is also used for drawing on a graph.

The N key is one of several keys that can perform three
operations, depending on whether you first press 2 or ¥.

The following

example shows using the 2 or ¥ modifier key

TI-89

with the N key.

2 K

QUIT

accesses

, which is the

same color as the

The following
key with the

2 

accesses

(convert). The

convert symbol is

the same color as

the 2 key.

2

key.

N

TI-92 Plus

alphabetic key.

Y

example shows using the 2 or ¥ modifier

ú

primary key types

QUIT PASTE

ESC

accesses the

key’s primary

function.

ú

TABLE

Y

Pressing the

the letter Y.

¥ 7

which is the same color as
the ¥ key.

¥ '

Table screen. The word is
the same color as the
key.

accesses

displays the

PASTE

¥

,

18 Chapter 2: Operating the Calculator

Some keys perform only one additional operation, which may require
either 2 or ¥, depending on the color in which the operation is
printed on the keyboard and where it is positioned above the key.

Other Important
Keys You Need to
Be Familiar With

Some keystrokes

Note:

differ between the
the

TI-92 Plus

Keystroke Differences table
in the front of this guidebook
for a complete list.

. See the

TI-89

and

On the TI-89, ¥

CUT

2nd

accesses
is the same color as
the ¥ key.

When you press a modifier such as 2 or ¥, a

or 2 indicator

2ND

CUT

5

, which

appears in the status line at the bottom of the display. If you press a
modifier by accident, press it again (or press N) to cancel its
effect.

Key Description

¥ #

¥ $

¥ %

¥ &

¥ '

TI.89:

5

¥

6

¥

7

¥

TI.92 Plus:

¥

X

(cut)

¥

C

(copy)

¥

V

(paste)

Displays the Y= Editor (Chapter 6).

Displays the Window Editor (Chapter 6).

Displays the Graph screen (Chapter 6).

Sets parameters for the Table screen (Chapter 13).

Displays the Table screen (Chapter 13).

These keys let you edit entered information by
performing a cut, copy, or paste operation.

2 a

2 ¾

2 

TI.89:



¥

TI.92 Plus:



2

0

2 /

¥ 8

Switches the active side in a split screen (Chapter 14).

Toggles the custom menu on and off (page 37).

Converts measurement units (Chapter 4).

Designates a measurement unit (Chapter 4).

Deletes the character to the left of the cursor
(backspaces).

Toggles between insert and overtype mode for
entering information (page 33).

Deletes the character to the right of the cursor.

Chapter 2: Operating the Calculator 19

Important Keys
(continued)

Key Description
TI.89:

Í

TI.92 Plus:

Í

2

2 <

Enters the “with” operator, which is used in symbolic
calculations (Chapter 3).

,

Performs integrations and derivatives (Chapter 3).

2 =

2 ’

2 I

2 ¯

2
°

2 £

TI.89:

9

2

TI.92 Plus:

À

¥

2 ¿

2 ±

,

2 ²

Designates an angle in polar, cylindrical, and spherical
coordinates.

Displays the

Displays the

Displays the

menu.

MATH
MEMORY
VAR-LINK

screen (Chapter 21).

screen for managing variables

and Flash applications (Chapter 21).

Recalls the contents of a variable (page 48).

Displays the

Displays the

dialog box (Chapter 4).

UNITS

menu, which lets you select Greek

CHAR

letters, international accented characters, etc.
(Chapter 18).

Recalls the previous entry and the last answer,
respectively (page 49).

20 Chapter 2: Operating the Calculator

Entering Alphabetic Characters

Alphabetic characters are used in expressions such as xñ+yñ,
to enter variable names (page 47), and in the Text Editor
(Chapter 18).

Entering a Letter
Character on the
TI.89

Typing Alphabetic
Characters on the
TI.89 / TI.92 Plus

On the

Note:

not need j or alpha-lock
to type x, y, z, or t. But you
must use ¤ or uppercase

-lock for X, Y, Z, or T.

ALPHA

TI-89

, you do

The letters x, y, z, and t are commonly used in algebraic expressions.
So that you can type them quickly, these letters are primary keys on
the

Other letters are available as the

TI-89

keyboard.

X Y Z T

j

function of another key,
similar to the 2 and ¥ modifiers described in the previous section.
For example:

2 È

types

, which is

the same color as the

To: On the TI.89, press: On the TI.92 Plus, press:

Type a single
lowercase
alpha

´

2

key.

j

and then the letter
key
(status line shows

´

A

=

)

j

[A] types an A,
which is the same
color as the j key.

the letter key

character.
Type a single

uppercase

¤

and then the letter key

(status line shows +)

¤

and then the letter key

(status line shows +)
alpha
character.

Type a space.

j 

(alpha function

spacebar

of the · key)

On the

Note:

lock is always turned off
when you change
applications, such as going
from the Text Editor to the
Home screen.

TI-89

, alpha-

Turn on
lowercase
alpha-lock.

Turn on
uppercase
ALPHA-lock.

Turn off alpha­lock.

2 ™

(status line shows

¤ ™

(status line shows

j

(turns off upper-

and lowercase lock)

Chapter 2: Operating the Calculator 21

(no action needed)

)

2 ¢

)

2 ¢

uppercase lock)

(turns off

Typing Alphabetic
Characters …
(continued)

On the

To type a period, comma, or other character that is the primary

¦

, while either type of alpha-lock is on:

TI-89

function of a key, you must turn alpha-lock off.
To type a second function character such as 2 [, you do not

¦

need to turn alpha-lock off. After you type the character, alpha­lock remains on.

Automatic Alpha­Lock in TI.89 Dialog
Boxes

To type a number,

Note:

press
lock off. Press

2 ™

letters.

to turn alpha-

j

j

to resume typing

or

There are certain times when you do not need to press

2 ™

to type alphabetic characters on the

TI-89

j

or

. Automatic
alpha-lock is turned on whenever a dialog box is first displayed. The
automatic alpha-lock feature applies to these dialog boxes:

Dialog box Alpha-lock

Catalog dialog box

All commands are listed in alphabetical
order. Press a letter to go to the first
command that begins with that letter. See
page 44 for more information.

Units dialog box

In each unit category, type the first letter of a
unit or constant. See Chapter 4 for more
information.

Dialog boxes with entry
fields

These include, but are not limited to:

New Folder

,

Rename

, and

Save Copy As

Create

. See
page 35 for more information about dialog
boxes.

Alpha-lock is

turned on in dialog boxes that require numeric-

not

only entries. The dialog boxes that accept only numeric entries are:

Resize Matrix, Zoom Factors

, and

Table Setup

.

For Special
Characters

Use the 2
characters. For more information, refer to “Entering Special
Characters” in Chapter 18.

22 Chapter 2: Operating the Calculator

¿

menu to select from a variety of special

Home Screen

Displaying the
Home Screen

Parts of the Home
Screen

When you first turn on your

TI-89 / TI-92 Plus

, the Home screen
is displayed. The Home screen lets you execute instructions,
evaluate expressions, and view results.

When you turn on the

2

®

, the display always shows the Home screen. (If the

TI-89 / TI-92 Plus

turned itself off through APDé, the display shows the

TI-89 / TI-92 Plus

after it has been turned off with

previous screen, which may or may not have been the Home screen.)
To display the Home screen at any time:

Press:

¦

"

TI.89:
TI.92 Plus:

¥"

— or —

2K

Press

¦

— or —
Press:

¦

O j

TI.89:
TI.92 Plus:

O

A
A

The following example gives a brief description of the main parts of
the Home screen.

History Area

Lists entry/answer pairs
you have entered.

Pretty Print Display

Shows exponents,
roots, fractions, etc.,
in traditional form.
Refer to page 29.

Last Entry

Your last entry.

Entry Line

Where you enter
expressions or
instructions.

History Area

Toolbar

Press ƒ, „, etc., to
display menus for selecting
operations.

Last Answer

Result of your last entry.
Note that results are not
displayed on the entry line.

Status Line

Shows the current state
of the TI-89 / TI-92 Plus.

The history area shows up to eight previous entry/answer pairs
(depending on the complexity and height of the displayed
expressions). When the display is filled, information scrolls off the
top of the screen. You can use the history area to:

Review previous entries and answers. You can use the cursor to

¦

view entries and answers that have scrolled off the screen.
Recall or auto-paste a previous entry or answer onto the entry

¦

line so that you can re-use or edit it. Refer to pages 50 and 52.

Chapter 2: Operating the Calculator 23

V

V

p

Scrolling through
the History Area

Normally, the cursor is in the entry line. However, you can move the
cursor into the history area.

To: Do this:

iew entries or answers
that have scrolled off
the screen

1. From the entry line, press Cto
highlight the last answer.

2. Continue using Cto move the
cursor from answer to entry, up
through the history area.

For an example of

Note:

viewing a long answer, refer
to page 28.

History Information
on the Status Line

Go to the oldest or newest
history pair

iew an entry or answer
that is too long for one
line (úis at end of line)

If the cursor is in the history area, press

¥ C

or ¥ D, respectively.

Move the cursor to the entry or answer.
Use A and B to scroll left and right (or

2 A

and 2 B to go to the beginning

or end), respectively.

Return the cursor to the
entry line

Press N, or press Duntil the cursor is
back on the entry line.

Use the history indicator on the status line for information about the
entry/answer pairs. For example:

If the cursor
is on the
entry line:

If the cursor
is in the
history area:

Total number of
pairs that are
currently saved.

8/30

Pair number of
the highlighted
entry or answer.

Maximum number
of pairs that can
be saved.

Total number of
pairs that are
currently saved.

By default, the last 30 entry/answer pairs are saved. If the history
area is full when you make a new entry (indicated by

30/30

), the new
entry/answer pair is saved and the oldest pair is deleted. The history
indicator does not change.

Modifying the
History Area

To: Do this:

Change the number of

airs that can be saved

Press ƒand select

TI.89:

¥Í

TI.92 Plus:

9:Format

¥

, or press

. Then

F

press B, use Cor Dto highlight the
new number, and press

Clear the history area
and delete all saved pairs

Delete a particular
entry/answer pair

24 Chapter 2: Operating the Calculator

Press ƒand select

ClrHome

enter

on the entry line.

Move the cursor to either the entry or
answer. Press 0or

¸

twice.

8:Clear Home

M

.

, or

p

Entering Numbers

The keypad lets you enter positive and negative numbers for
your calculations. You can also enter numbers in scientific
notation.

Entering a Negative
Number

|

for

Important:

subtraction and use

for negation.

·

Use

1. Press the negation key ·. (Do not use the subtraction key |.)

2. Type the number.
To see how the

TI-89 / TI-92 Plus

evaluates a negation in relation to
other functions, refer to the Equation Operating System (EOSé)
hierarchy in Appendix B. For example, it is important to know that

ñ

functions such as
Use cand dto include

are evaluated before negation.

x

Evaluated as ë(2ñ)

arentheses if you have
any doubt about how a
negation will be
evaluated.

If you use |instead of ·(or vice versa), you may get an error
message or you may get unexpected results. For example:

¦ 9

p·

ë

=

63

7

— but —

p|

¦ 6

9

displays an error message.

7

|

=

2

4

— but —

6 ·2 = ë12

·2 «

¦

since it is interpreted as

4 = 2

, implied multiplication.

6(ë2)

— but —

|2 «

subtracts 2 from the previous answer and then adds 4.

4

Entering a Number
in Scientific
Notation

1. Type the part of the number that precedes the exponent. This

value can be an expression.

2. Press:

^

TI.89:

2

TI.92 Plus:

E

appears in the display.

^

3. Type the exponent as an integer with up to 3 digits. You can use a

negative exponent.

Entering a number in scientific notation does not cause the answers
to be displayed in scientific or engineering notation.

The display format is determined by
the mode settings (pages 29 through

31) and the magnitude of the
number.

Represents 123.45 × 10

Chapter 2: Operating the Calculator 25

-2

Entering Expressions and Instructions

You perform a calculation by evaluating an expression. You
initiate an action by executing the appropriate instruction.
Expressions are calculated and results are displayed
according to the mode settings described on page 29.

Definitions

Appendix A describes

Note:

all of the
built-in functions and
instructions.

Note:

the word
generic reference to both
functions and instructions.

TI-89 / TI-92 Plus

This guidebook uses

command

as a

Expression Consists of numbers, variables, operators, functions,

and their arguments that evaluate to a single answer.

ñ

For example:

Enter an expression in the same order that it

¦

p

.

+

r

3

normally is written.
In most places where you are required to enter a

¦

value, you can enter an expression.

Operator Performs an operation such as +, ì, ù, ^.

Operators require an argument before and after the

¦

operator. For example:

4+5

and

5^2

.

Function Returns a value.

Functions require one or more arguments

¦

(enclosed in parentheses) after the function. For
example:

‡

(5)

and

min

(5,8)

.

Instruction Initiates an action.

Instructions cannot be used in expressions.

¦

Some instructions do not require an argument. For

¦

example:
Some require one or more arguments. For

¦

example:

ClrHome

Circle

0,0,5

.

.

For instructions, do not put the
arguments in parentheses.

The

Implied
Multiplication

26 Chapter 2: Operating the Calculator

TI-89 / TI-92 Plus

does not conflict with a reserved notation.

If you enter: The TI.89 / TI.92 Plus interprets it as:

Valid

Invalid

p

2
4 sin(46) 4ùsin(46)

5(1+2)
[1,2]a [a 2a]
2(a) 2ùa

xy
a(2)
a[1,2]

recognizes implied multiplication, provided it

p

ù

2

or

(1+2)5 5ù(1+2)

Single variable named

or

(1+2)ù5

xy

Function call
Matrix index to element

a[1,2]

g

g

Parentheses

Expressions are evaluated according to the Equation Operating
System (EOSé) hierarchy described in Appendix B. To change the
order of evaluation or just to ensure that an expression is evaluated
in the order you require, use parentheses.

Calculations inside a pair of parentheses are completed first. For
example, in
answer by

4

, EOS first evaluates

4(1+2)

.

and then multiplies the

(1+2)

Entering an
Expression

Example

You can also select

Note:

by using

log

TI.89:

½

TI.92 Plus:

(page 44).

2 ½

Type the expression, and then press

¸

to evaluate it. To enter a

function or instruction name on the entry line, you can:

2W

¦

Press its key, if available. For example, press

TI.92 Plus:

W.

TI.89:

— or —

¦

Select it from a menu, if available. For example, select
the

Number

submenu of the

MATH

menu.

— or —

¦

Type the name letter-by-letter from the keyboard. (On the

j

use

and 2

of uppercase or lowercase letters. For example, type

Calculate

On the TI.89: On the TI.92 Plus: Display

3.76

c·
«2]

5

dd

2

«
2™
c45d

¸¸

3.76 ÷ (ë7.9 + ‡5) + 2 log 45

e

7.9

LOG

j

™

to type letters.) You can use any mixture

Type the function name in this
example.

.

3.76

e

7.9

c·
«2]

5

dd

2

«

LOG

c45d

3.76/(ë7.9+‡(

2 ]

inserts ‡( because its

ar

ument must be in parentheses.

3.76/(ë7.9+‡(5))

Use d once to close ‡(5) and again
to close (ë7.9 + ‡5).

3.76/(ë7.9+‡(5))+2log(45)

log

requires ( ) around its ar

sin(

2:abs

or

or

from

TI-89

,

Sin(

ument.

.

Entering Multiple
Expressions on a
Line

To enter more than one
expression or instruction
at a time, separate them

Displays last result only.

with a colon by pressing

2Ë

.

!

is displayed when you press § to

store a value to a variable.

Chapter 2: Operating the Calculator 27

A

If an Entry or
Answer Is Too Long
for One Line

When you scroll to

Note:

the right, 7 is displayed at
the beginning of the line.

In the history area, if both the entry and its answer cannot be
displayed on one line, the answer is displayed on the next line.

If an entry or answer is too long to
fit on one line, úis displayed at the
end of the line.

To view the entire entry or answer:

1. Press Cto move the cursor from the entry line up into the history

area. This highlights the last answer.

2. As necessary, use Cand Dto highlight the entry or answer you

want to view. For example, Cmoves from answer to entry, up
through the history area.

3. Use Band Aor

2A

to scroll right and left.

2B

and

4. To return to the entry line, press N.

Continuing a
Calculation

Example

Stopping a
Calculation

When you press

TI-89 / TI-92 Plus

¸

to evaluate an expression, the

leaves the expression on the entry line and highlights
it. You can continue to use the last answer or enter a new
expression.

If you press: The TI.89 / TI.92 Plus:

«, |, p, e
Z

, or

§

,

Replaces the entry line with the variable
which lets you use the last answer as the
beginning of another expression.

ny other key Erases the entry line and begins a new entry.

Calculate

On the TI.89: On the TI.92 Plus: Display

3.76

2]5dd

«22™
c45d

¸

3.76 ÷ (ë7.9 + ‡5)

ec·

7.9

¸

LOG

«

j

When a calculation is in progress,

. Then add

ec·

3.76

2]5dd

«

2 LOG

c45d

¸

BUSY

2 log 45

7.9

¸

to the result.

«

When you press «, the entry
line is replaced with the
variable ans(1), which contains
the last answer.

appears on the right end of

the status line. To stop the calculation, press ´.
There may be a delay before the “break”

message is displayed.

ans(1)

,

Press Nto return to the current application.

28 Chapter 2: Operating the Calculator

Formats of Displayed Results

A result may be calculated and displayed in any of several
formats. This section describes the
and their settings that affect the display formats. To check or
change your current mode settings, refer to page 40.

TI-89 / TI-92 Plus

modes

Pretty Print Mode

Exact/Approx Mode

By retaining fractional

Note:

and symbolic forms,
reduces rounding errors that
could be introduced by
intermediate results in
chained calculations.

EXACT

By default,

Pretty Print = ON

. Exponents, roots, fractions, etc., are
displayed in the same form in which they are traditionally written.
You can use

p

ñ

p

,

2

3

to turn pretty print off and on.

Pretty Print

ON OFF

xì3

,

2

p

p

,

,

/2

^2

‡

((xì3)/2)

The entry line does not show an expression in pretty print. If pretty
print is turned on, the history area will show both the entry and its
result in pretty print after you press

By default,

Exact/Approx = AUTO

¸

.

. You can use

3

to select from

three settings.
Because

is a combination of

AUTO

the other two settings, you should be
familiar with all three settings.

EXACT

fractional or symbolic form (

— Any result that is not a whole number is displayed in a

, p, 2, etc.).

1/2

Shows whole-number results.

Shows simplified fractional results.

Shows symbolic p.

Shows symbolic form of roots that
cannot be evaluated to a whole
number.

Press ¥
override the
display a floating-point result.

Chapter 2: Operating the Calculator 29

¸

to temporarily

EXACT

setting and

Exact/Approx
(continued)

Results are rounded

Note:

to the precision of the

TI-89 / TI-92 Plus

displayed according to
current mode settings.

and

APPROXIMATE

— All numeric results, where possible, are displayed

in floating-point (decimal) form.

Fractional results are
evaluated numerically.

Symbolic forms, where
possible, are evaluated
numerically.

Because undefined variables cannot be evaluated, they are
treated algebraically. For example, if the variable

p

rñ= 3.14159⋅r

AUTO

— Uses the

APPROXIMATE

certain functions may display

ñ

.

form where possible, but uses the

EXACT

form when your entry contains a decimal point. Also,

APPROXIMATE

results even if your

r

entry does not contain a decimal point.

is undefined,

To retain an

Tip:

form, use fractions instead
of decimals. For example,
use 3/2 instead of 1.5.

To evaluate an entry in

Tip:

APPROXIMATE

regardless of the current
setting, press

EXACT

form,

¥¸

.

A decimal in the entry forces a
floating-point result.

The following chart compares the three settings.

Exact

Entry

Result

8/4 2 2. 2
8/6 4/3 1.33333 4/3

8.5ù3 51/2 25.5 25.5

‡

(2)/2

p

ù

22

p

ù

2. 2

2

2

⋅

p

⋅

p

Approximate

Result

.707107

6.28319 2

6.28319 6.28319

Auto

Result

2

A decimal in the
entry forces a
floating-point

2

result in

⋅

p

AUTO

.

30 Chapter 2: Operating the Calculator

Display Digits Mode

By default,

Display Digits = FLOAT 6

rounded to a maximum of six digits. You can use

, which means that results are

3

to select

different settings. The settings apply to all exponential formats.

Regardless of the

Note:

Display Digits setting, the
full value is used for internal
floating-point calculations to
ensure maximum accuracy.

A result is

Note:

automatically shown in
scientific notation if its
magnitude cannot be
displayed in the selected
number of digits.

Exponential Format
Mode

Internally, the

TI-89 / TI-92 Plus

calculates and retains all decimal
results with up to 14 significant digits (although a maximum of 12 are
displayed).

Setting Example Description

FIX
(0 – 12)

FLOAT 123.456789012

123. (FIX 0)

123.5 (FIX 1)

123.46 (FIX 2)

123.457 (FIX 3)

Results are rounded to the
selected number of decimal
places.

Number of decimal places varies,
depending on the result.

FLOAT
(1 – 12)

By default,
You can use

1.E 2 (FLOAT 1)

E

1.2

2 (FLOAT 2)

123. (FLOAT 3)

123.5 (FLOAT 4)

123.46 (FLOAT 5)

123.457 (FLOAT 6)

Exponential Format = NORMAL

3

to select from three

Results are rounded to the total
number of selected digits.

.

settings.

In the history area, a

Note:

number in an entry is
displayed in
its absolute value is less
than .001.

SCIENTIFIC

Setting Example Description

NORMAL 12345.6

if

If a result cannot be displayed in the
number of digits specified by the

Display Digits

TI-89 / TI-92 Plus

NORMAL

mode, the

to

SCIENTIFIC

switches from

for that

result only.

SCIENTIFIC 1.23456E 4 1.23456 × 10

4

Exponent (power of 10).
Always 1 digit to the left of the

decimal point.

ENGINEERING 12.3456

E

3 12.3456 × 10

3

Exponent is a multiple of 3.
May have 1, 2, or 3 digits to the

left of the decimal point.

Chapter 2: Operating the Calculator 31

A

A

Editing an Expression in the Entry Line

A

B

Knowing how to edit an entry can be a real time-saver. If you
make an error while typing an expression, it’s often easier to
correct the mistake than to retype the entire expression.

Removing the
Highlight from the
Previous Entry

Moving the Cursor

If you accidentally

Note:

press
the cursor moves up into the
history area. Press Nor
press Duntil the cursor
returns to the entry line.

instead of Aor B,

C

After you press

¸

to evaluate an expression, the

TI-89 / TI-92 Plus

leaves that expression on the entry line and highlights it. To edit the
expression, you must first remove the highlight; otherwise, you may
clear the expression accidentally by typing over it.

To remove the highlight,
move the cursor toward
the side of the expression
you want to edit.

moves the cursor to the end

of the expression.

moves the cursor to the beginning.

After removing the highlight, move the cursor to the applicable
position within the expression.

To move the cursor: Press:

Left or right within an expression.

or

B

Hold the pad to
repeat the
movement.

To the beginning of the expression.
To the end of the expression.

2A

2B

Deleting a Character

To delete: Press:

The character to the
left of the cursor.

The character to the
right of the cursor.

ll characters to the

right of the cursor.

Clearing the Entry
Line

To clear the entry line, press:

M

¦

if the cursor is at the beginning or end of the entry line.

— or —

MM

¦

entry line. The first press deletes all characters to the right of the
cursor, and the second clears the entry line.

32 Chapter 2: Operating the Calculator

0

Hold 0to delete multiple
characters.

¥0

M

(once only)

If there are no characters to the
right of the cursor,

M

erases

the entire entry line.

if the cursor is not at the beginning or end of the

Inserting or
Overtyping a
Character

Look at the cursor to

Tip:

see if you’re in insert or
overtype mode.

The

TI-89 / TI-92 Plus

default, the

TI-89 / TI-92 Plus

the insert and overtype modes, press

If the TI.89 / TI.92 Plus is in: The next character you type:

has both an insert and an overtype mode. By

is in the insert mode. To toggle between

2/

.

Will be inserted at the cursor.

Thin cursor between
characters

Will replace the highlighted

Cursor highlights a
character

character.

Replacing or
Deleting Multiple
Characters

When you highlight

Tip:

characters to replace,
remember that some
function keys automatically
add an open parenthesis.

First, highlight the applicable characters. Then, replace or delete all
the highlighted characters.

To: Do this:

Highlight multiple
characters

1. Move the cursor to either side of the
characters you want to highlight.

To replace
cursor beside

sin(

with

sin

.

cos(

, place the

2. Hold ¤and press Aor Bto highlight
characters left or right of the cursor.

Hold ¤ and press B B B B.

Replace the

Type the new characters.
highlighted
characters

— or —
Delete the

highlighted
characters

Press 0.

Chapter 2: Operating the Calculator 33

A

Menus

Displaying a Menu

To leave the keyboard uncluttered, the

TI-89 / TI-92 Plus

menus to access many operations. This section gives an
overview of how to select an item from any menu. Specific
menus are described in the appropriate chapters of this
guidebook.

Press: To display:

ƒ, „

etc.

,

toolbar menu — Drops down from the toolbar at the
top of most application screens. Lets you select
operations useful for that application.

O

APPLICATIONS

menu — Lets you select from a list of

applications. Refer to page 38.

2¿

menu — Lets you select from categories of

CHAR

special characters (Greek, math, etc.).

2I

menu — Lets you select from categories of

MATH

math operations.

TI.89:

½

TI.92 Plus:

2½

CATALOG

alphabetic list of the
functions and instructions. Also lets you select user­defined functions or Flash application functions (if
any have been defined or loaded).

menu — Lets you select from a complete,

TI-89 / TI-92 Plus’s

built-in

uses

Selecting an Item
from a Menu

2¾

CUSTOM

menu — Lets you access a menu that you
can customize to list any available function,
instruction, or character. The

TI-89 / TI-92 Plus

includes
a default custom menu, which you can modify or
redefine. Refer to page 37 and to Chapter 17.

To select an item from the displayed menu, either:

Press the number or letter shown to the left of that item. For a

¦

letter on the

TI-89

, press

j

and then a letter key.
— or —
Use the cursor pad Dand Cto highlight the item, and then press

¦

¸

. (Note that pressing Cfrom the first item moves the

highlight to the last item, and vice versa.)

6

indicates that a menu will drop down

from the toolbar when you press „.

To select
This closes the menu and inserts the
function at the cursor location.

factor

factor(

, press 2 or D

¸

.

34 Chapter 2: Operating the Calculator

Items Ending with

ú

(Submenus)

Because of limited

Note:

screen size, the
overlaps these menus as:

TI-89

If you select a menu item ending with ú, a submenu is displayed. You
then select an item from the submenu.

For example,
submenu that lets you select a
specific List function.

ï

indicates that you can use
the cursor pad to scroll down
for additional items.

List

displays a

For items that have a submenu, you can use the cursor pad as
described below.

¦

To display the submenu for the highlighted item, press B.
(This is the same as selecting that item.)

¦

To cancel the submenu without making a selection, press A.
(This is the same as pressing N.)

¦

To wrap to the last menu item directly from the first menu item,
press C. To wrap to the first menu item directly from the last
menu item, press D.

Items Containing “. . .”
(Dialog Boxes)

Canceling a Menu

If you select a menu item containing “

” (ellipsis marks), a dialog

. . .

box is displayed for you to enter additional information.

For example,
displays a dialog box that prompts
you to select a folder name and
type a variable name.

After typing in an input box such as Variable, you must

¸

press
dialog box.

twice to save the information and close the

Save Copy As ...

"

indicates that you can press B to

display and select from a menu.

An input box indicates that you
must type a value. (Alpha-lock is
automatically turned on for the
TI-89. See page 22.)

To cancel the current menu without making a selection, press N.
Depending on whether any submenus are displayed, you may need to
press Nseveral times to cancel all displayed menus.

Chapter 2: Operating the Calculator 35

Moving from One
Toolbar Menu to
Another

To move from one toolbar menu to another without making a
selection, either:

¦

Press the key (ƒ, „, etc.) for the other toolbar menu.
— or —

¦

Use the cursor pad to move to the next (press B) or previous
(press A) toolbar menu. Pressing Bfrom the last menu moves to
the first menu, and vice versa.

When using B, be sure that an item with a submenu is not
highlighted. If so, Bdisplays that item’s submenu instead of moving
to the next toolbar menu.

Example: Selecting
a Menu Item

Round the value of p to three decimal places. Starting from a clear
entry line on the Home screen:

1. Press

2. Press

2I

to display the

1

to display the

submenu. (Or press

Number

¸

MATH

since

menu.

the first item is automatically
highlighted.)

3. Press

DD

4. Press

¸

to select

3

¸

and

2T

to evaluate the expression.

round

.)

b3 d

. (Or press

and then

Selecting the function in
Step 3 automatically

round(

typed
entry line.

on the

36 Chapter 2: Operating the Calculator

Using the Custom Menu

Turning the Custom
Menu On and Off

You can also turn the

Note:

custom menu on and off by
entering

CustmOff

and pressing

Tip:

give you quick access to
commonly used items.
Chapter 17 shows you how
to create custom menus for
the items you use most
often.

CustmOn

in the entry line

A custom menu can

¸

or

.

The

TI-89 / TI-92 Plus

has a custom menu that you can turn on
and off at any time. You can use the default custom menu or
create your own as described in Chapter 17: Programming.

When you turn on the custom menu, it replaces the normal toolbar
menu. When you turn it off, the normal menu returns. For example,
from the Home screen’s normal toolbar menu, press 2

¾

to

toggle the custom menu on and off.

2 ¾

Home screen normal toolbar menu Custom menu

Unless the menu has been modified, the default custom menu
appears.

Menu Function

ƒ

Var

„

f(x)

…

Solve

†

Unit

‡

Symbol

Internat’l

TI.89:

2

TI.92 Plus:

Tool

2 ‰

TI.89:
TI.92 Plus:

ˆ

ˆ

‰

Common variable names.
Function names such as f(x), g(x), and f(x,y).

Items related to solving equations.
Common units such as _m, _ft, and _l.
Symbols such as #, ?, and ~.
Commonly accented characters such as è, é,and ê.

ClrHome, NewProb

, and

CustmOff

.

Restoring the
Default Custom
Menu

The previous custom

Note:

menu is erased. If that menu
was created with a program
(Chapter 17), it can be
recreated later by running
the program again.

If a custom menu other than the default is displayed and you want to
restore the default:

1. From the Home screen, use 2

¾

to turn off the custom

menu and display the Home screen’s normal toolbar menu.

2. Display the
and select

2 ˆ

TI.89:
TI.92 Plus:

Clean Up

3:Restore custom default

ˆ

toolbar menu,

.

This pastes the commands used to create the default menu into
the entry line.

3. Press

¸

to execute the commands and restore the default.

Chapter 2: Operating the Calculator 37

v

Selecting an Application

From the

APPLICATIONS

To cancel the menu

Note:

without making a selection,
press

N

.

Menu

The

TI-89 / TI-92 Plus

has different applications that let you
solve and explore a variety of problems. You can select an
application from a menu, or you can access commonly used
applications directly from the keyboard.

1. Press

O

to display a menu that lists the applications.

2. Select an application. Either:

¦

Use the cursor pad Dor Cto
highlight the application and
then press

¸

.

— or —

¦

Press the number or letter for
that application.

Application: Lets you:

FlashApps
Y= Editor

Display a list of Flash applications, if any.
Define, edit, and select functions or

equations for graphing (Chapters 6 – 11).

Window Editor

Set window dimensions for viewing a graph
(Chapter 6).

Graph
Table

Data/Matrix Editor

Program Editor

Text Editor
Numeric Solver

Home

Display graphs (Chapter 6).
Display a table of variable values that

correspond to an entered function
(Chapter 13).

Enter and edit lists, data, and matrices. You
can perform statistical calculations and
graph statistical plots (Chapters 15 and 16).

Enter and edit programs and functions
(Chapter 17).

Enter and edit a text session (Chapter 18).
Enter an expression or equation, define

alues for all but one variable, and then solve

for the unknown variable (Chapter 19).
Enter expressions and instructions, and

perform calculations.

38 Chapter 2: Operating the Calculator

From the Keyboard

You can access commonly used applications from the keyboard. On
the

for example, ¥ # is the same as pressing ¥ and then ƒ.

TI-89

This guidebook uses the notation ¥ #, similar to the notation used
in second functions.

Application: Press:

Home

Y= Editor

"

TI.89:
TI.92 Plus:

¥ #

¹

"

Applications listed
above ƒ, „ etc.,
are printed in the
same color as ¥.

TI-89

Window Editor¥
Graph
Table Setup
Table Screen

On the

TI-92 Plus

¥ %

¥ &

¥ '

, applications are listed above the

Applications

$

Diamond key

WINDOW GRAPH TBLSet TABLEY=

F1 F2 F3 F4 F5

APPS

HOME

QWERTY

keys.

Chapter 2: Operating the Calculator 39

Setting Modes

Checking Mode
Settings

Indicates you can
scroll down to see
additional modes.

Modes control how numbers and graphs are displayed and
interpreted. Mode settings are retained by the Constant
Memoryé feature when the

TI-89 / TI-92 Plus

is turned off. All
numbers, including elements of matrices and lists, are
displayed according to the current mode settings.

3

Press

to display the

dialog box, which lists the modes

MODE

and their current settings.

There are three pages of mode listings.
Press ƒ, „, or … to quickly display a
particular page.

!

indicates that you can
press B or A to display
and select from a menu.

Changing Mode
Settings

To cancel a menu and

Tip:

return to the
box without making a
selection, press N.

MODE

dialog

Modes that are not currently valid are dimmed. For example,

Note:

on Page 2,

Split 2 App

is not valid when

Split Screen

=

FULL

. When you

scroll through the list, the cursor skips dimmed settings.

From the

MODE

dialog box:

1. Highlight the mode setting you want to change. Use Dor C(with

ƒ, „

, or …) to scroll through the list.

2. Press Bor Ato display a menu that lists the valid settings. The
current setting is highlighted.

3. Select the applicable setting. Either:

¦

Use Dor Cto highlight the setting and press

¸

.

— or —

¦

Press the number or letter for that setting.

4. Change other mode settings, if necessary.

5. When you finish all your changes, press

¸

to save the

changes and exit the dialog box.

Important:

If you press Ninstead of

¸

to exit the

MODE

dialog box, any mode changes you made will be canceled.

40 Chapter 2: Operating the Calculator

A

A

Overview of the
Modes

For detailed

Note:

information about a
particular mode, look in the
applicable section of this
guidebook.

Mode Description

Graph

Current
Folder

Type of graphs to plot:

POLAR, SEQUENCE, 3D

Folder used to store and recall variables. Unless you
have created additional folders, only the
is available. Refer to “Using Folders to Store
Independent Sets of Variables” in Chapter 5.

Display
Digits

Maximum number of digits (
of decimal places (
result. Regardless of the setting, the total number of
displayed digits in a floating-point result cannot
exceed 12. Refer to page 31.

Angle

Units in which angle values are interpreted and
displayed:

Exponential
Format

Complex
Format

Notation used to display results:

SCIENTIFIC

Format used to display complex results, if any:

(complex results are not displayed unless you

REAL

use a complex entry),

Vector
Format

Pretty Print

Format used to display 2- and 3-element vectors:

RECTANGULAR, CYLINDRICAL

Turns the pretty print display feature
Refer to page 29.

Split Screen

Splits the screen into two parts and specifies how the
parts are arranged:

TOP-BOTTOM

Split 1 App

pplication in the top or left side of a split screen. If you

are not using a split screen, this is the current application.

Split 2 App

pplication in the bottom or right side of a split

screen. This is active only for a split screen.

Number of
Graphs

Graph 2

For a split screen, lets you set up both sides of the
screen to display independent sets of graphs.

If

Number of Graphs = 2

the Split 2 part of the screen. Refer to Chapter 12.

Split Screen
Ratio

Exact/Approx

Proportional sizes of the two parts of a split screen:

1:1, 1:2

, or

Calculates expressions and displays results in
numeric form or in rational/symbolic form:

EXACT

, or

FUNCTION, PARAMETRIC

) displayed in a floating-point

FIX

RADIAN

, or

or

DEGREE

ENGINEERING

RECTANGULAR

FULL

, or

LEFT-RIGHT

, selects the type of graph in

. (

TI-92 Plus

2:1

APPROXIMATE

, or DE.

) or fixed number

FLOAT

.

NORMAL

. Refer to page 31.

, or

, or

SPHERICAL

OFF

(no split screen),

. Refer to Chapter 14.

only)

. Refer to page 29.

MAIN

,

POLAR

or ON.

AUTO

,

folder

.

.

,

Chapter 2: Operating the Calculator 41

Modes
(continued)

Mode Description

Base

Unit System

Lets you perform calculations by entering numbers in
decimal

(DEC)

Lets you enter a unit for values in an expression,
such as 6_m * 4_m or 23_m/_s * 10_s, convert values
from one unit to another within the same category,
and create your own user-defined units.

Custom Units

Lets you select custom defaults. The mode is dimmed
until you select

Language

Lets you localize the
several languages, depending on which language
Flash applications are installed.

, hexadecimal

Unit System, 3:CUSTOM

TI-89 / TI-92 Plus

(HEX)

, or binary

(BIN)

.

into one of

form.

42 Chapter 2: Operating the Calculator

v

Using the Clean Up Menu to Start a New Problem

On the Home screen, the Clean Up toolbar menu lets you start
a new calculation from a cleared state without resetting the

TI-89 / TI-92 Plus’s

memory.

Clean Up Toolbar
Menu

When defining a

Tip:

variable that you want to
retain, use more than one
character in the name. This
prevents it from being
deleted inadvertently by

1:Clear a–z

.

From the Home screen, display the

2

ˆ

ˆ

Clears (deletes) all single-character variable names in

TI.89:
TI.92 Plus:

Menu Item Description

Clear a–z

the current folder, unless the variables are locked or
archived. You will be prompted to press
confirm the action.

Single-character variable names are often used in
symbolic calculations such as:

solve(aøxñ+bøx+c=0,x)

If any of the variables have already been assigned a

alue, your calculation may produce misleading
results. To prevent this, you can select
before beginning the calculation.

Clean Up

menu by pressing:

¸

1:Clear a–z

to

For information about

Note:

checking and resetting
memory or other system
defaults, refer to
Chapter 21.

NewProb

Places
press

NewProb

begin a new problem from a cleared state without

NewProb

¸

in the entry line. You must then

to execute the command.

performs a variety of operations that let you

resetting the memory:

¦

Clears all single-character variable names in the
current folder (same as

1:Clear a–z

), unless the

variables are locked or archived.

FnOff

and

,

Restore
custom
default

¦

Turns off all functions and stat plots (

PlotsOff

¦

Performs

ClrIO

) in the current graphing mode.

ClrDraw, ClrErr, ClrGraph, ClrHome

ClrTable

, and

.

If a custom menu other than the default is in effect,
this lets you restore the default. Refer to page 37.

Chapter 2: Operating the Calculator 43

Using the Catalog Dialog Box

Displaying the
CATALOG

The

CATALOG

TI-89 / TI-92 Plus

one convenient list. In addition, the

provides a way to access any built-in

command (functions and instructions) from

CATALOG

dialog box lets
you select functions used in Flash applications or user-defined
functions (if any have been loaded or defined).

To display the

½

TI.89:
TI.92 Plus:

The

CATALOG

CATALOG

½

2

defaults to „
list of all pre-installed
instructions)

ƒ

Help is reserved for
a future online help
Flash application.

.

Defaults to

„

Built-in.

dialog box, press:

, which displays an alphabetic

Built-in

TI-89 / TI-92 Plus

…

and † allow access to
Flash application functions and
User-Defined functions and
programs.

commands (functions and

Selecting a Built-in
Command from the

CATALOG

The first time you

Note:

display the
starts at the top of the list.
The next time you display
the list, it starts at the same
place you left it.

Built-in list

, it

Options that are not currently valid are dimmed. For

Note:

example,
application.
Flash application.

ƒ

Help

…

is reserved for a future online help Flash

Flash Apps

†

is dimmed if you have not installed a

User-Defined

is dimmed if you have not

created a function or a program.

When you select a command, its name is inserted in the entry line at
the cursor location. Therefore, you should position the cursor as
necessary before selecting the command.

1. Press:

½

TI.89:
TI.92 Plus:

2. Press „

2

Built-in

½

.

Commands are listed in

¦

alphabetical order. Commands that
do not start with a letter
(+, %, ‡, G, etc.) are at the end of
the list.

To exit the

¦

CATALOG

without

selecting a command, press N.

44 Chapter 2: Operating the Calculator

D

From the top of the list,

Tip:

press
bottom. From the bottom,
press D to move to the top.

to move to the

C

3. Move the úindicator to the command, and press

To move the úindicator: Press or type:

One command at a time
One page at a time
To the first command that

begins with a specified letter

C

or

2D

or

2C

The letter key. (On the

j

press

not

you need to press

2 ™

again before you can

type a letter.)

¸

.

, do

TI-89

first. If you do,

j

or

Information about
Parameters

For details about the

Note:

parameters, refer to that
command’s description in
Appendix A.

Selecting a Flash
Application
Function

For the command indicated by ú, the status line shows the required
and optional parameters, if any, and their type.

Indicated command
and its parameters

Brackets [ ] indicate
optional parameters.

From the example above, the syntax for

factor

expression

(

)

required

factor

is:

— or —

factor

expression,variable

(

)

optional

A Flash application may contain one or more functions. When you
select a function, its name is inserted in the entry line at the cursor
location. Therefore, you should position the cursor as necessary
before selecting the function.

1. Press:

½

TI.89:
TI.92 Plus:

2

½

2. Press

…

Flash Apps.

(This option is dimmed if no Flash

applications are installed in the

TI-89 / TI-92 Plus

The list is alphabetized by function

¦

.)

name. The left column lists functions.
The right column lists the Flash
application that contains the function.

Information about a function is

¦

displayed in the status line.
To exit without selecting a function,

¦

press N.

Chapter 2: Operating the Calculator 45

3. Move the úindicator to the function, and press

D

D

p

To move the úindicator: Press or type:

One function at a time

or

C

¸

.

Selecting a
User-Defined
Function or
Program

Use the VAR-LINK

Note:

screen to manage
variables, folders, and
Flash applications. See
Chapter 21.

One page at a time
To the first function that

begins with a specified letter

2D

The letter key. (On the

not

you need to press

2 ™

2C

or

j

press

first. If you do,

again before you can

j

TI-89

or

, do

type a letter.)

You can create your own functions or programs and then use

†

User-Defined

to access them. For instructions on how to create
functions, see “Creating and Evaluating User-Defined Functions” in
Chapter 5, and “Overview of Entering a Function” in Chapter 17. See
Chapter 17 for instructions on how to create and run a program.

When you select a function or program, its name is inserted in the
entry line at the cursor location. Therefore, you should position the
cursor as necessary before selecting the function or program.

1. Press:

½

TI.89:
TI.92 Plus:

2. Press

†

½

2

User-Defined.

(This option is dimmed if you have not

defined a function or created a program.)

The list is alphabetized by function /

¦

program name. The left column lists
functions and programs. The right
column lists the folder that contains
the function or program.

If the function or program’s first line is

¦

a comment, the comment text is
displayed in the status line.

To exit without selecting a function or

¦

program, press N.

3. Move the úindicator to the function or program, and press

¸

.

To move the úindicator: Press or type:

One function or program at a
time

One page at a time
To the first function or

rogram that begins with a

specified letter

46 Chapter 2: Operating the Calculator

C

or

2D

or

2C

The letter key. (On the

j

press

not

you need to press

2 ™

first. If you do,

j

again before you can

type a letter.)

TI-89

or

, do

Storing and Recalling Variable Values

When you store a value, you store it as a named variable. You
can then use the name instead of the value in expressions.
When the

TI-89 / TI-92 Plus

expression, it substitutes the variable’s stored value.

encounters the name in an

Rules for Variable
Names

Examples

A variable name:

¦

Can use 1 to 8 characters consisting of letters and digits. This
includes Greek letters (but not p), accented letters, and
international letters. Do not include spaces.

−

The first character cannot be a digit.

¦

Can use uppercase or lowercase letters. The names

, and

aB22

¦

Cannot be the same as a name that is preassigned by the

TI-89 / TI-92 Plus

−

Built-in functions (such as

LineVert

−

System variables (such as

all refer to the same variable.

ab22

. Preassigned names include:

abs

). Refer to Appendix A.

xmin

) and instructions (such as

and

, which are used to

xmax

AB22, Ab22

store graph-related values). Refer to Appendix B for a list.

Variable Description

myvar
a
Log
Log1
3rdTotal
circumfer

OK
OK
Not OK, name is preassigned to the
OK
Not OK, starts with a digit.
Not OK, more than 8 characters.

log

function.

,

Data Types

You can save any
data types, refer to

Data Types Examples

Expressions
Lists

Matrices

Character strings

TI-89 / TI-92 Plus

getType()

in Appendix A. Some examples are:

2.54, 1.25í6, 2p, xmin/10, 2+3i, (xì2)ñ, 2/2
{2 4 6 8}, {1 1 2}

[]

,

[1 0 0]

“Hello”, “The answer is:”, “xmin/10”

Pictures

Functions

myfunc(arg), ellipse(x,y,r1,r2)

Chapter 2: Operating the Calculator 47

data type as a variable. For a list of

1 0 0
3 4 6

v

Storing a Value in a

g

Variable

users should

Note:

TI-89

use j as necessary
when typing variable names.

1. Enter the value you want to store, which can be an expression.

2. Press

§

. The store symbol (!) is displayed.

3. Type the variable name.

4. Press

¸

.

To store to a variable temporarily, you can use the “with” operator.
Refer to “Substituting Values and Setting Constraints” in Chapter 3.

Displaying a
Variable

Refer to Chapter 3 for

Note:

information about symbolic
manipulation.

Using a Variable in
an Expression

To view a list of existin

Tip:

variable names, use

2°

Chapter 21.

as described in

Recalling a
Variable’s Value

1. Type the variable name.

2. Press

¸

.

If the variable is undefined, the variable name is shown in the result.
In this example, the variable

is

a

undefined. Therefore, it is used as a
symbolic variable.

1. Type the variable name into the

expression.

2. Press

¸

expression.

to evaluate the

The variable’s value
did not change.

If you want the result to replace the

ariable’s previous value, you must

store the result.

In some cases, you may want to use a variable’s actual value in an
expression instead of the variable name.

1. Press

2£

to display a dialog

box.

2. Type the variable name.

3. Press

In this example, the value stored in

¸

twice.

will be inserted at the

num1

cursor position in the entry line.

48 Chapter 2: Operating the Calculator

Reusing a Previous Entry or the Last Answer

You can reuse a previous entry by reexecuting the entry
“as is” or by editing the entry and then reexecuting it. You can
also reuse the last calculated answer by inserting it into a new
expression.

Reusing the
Expression on the
Entry Line

Reexecuting an entry

Tip:

“as is” is useful for iterative
calculations that involve
variables.

When you press

¸

to evaluate an expression, the

TI-89 / TI-92 Plus

leaves that expression on the entry line and highlights it. You can
type over the entry, or you can reuse it as necessary.

For example, using a variable, find the square of

1, 2, 3

, etc.

As shown below, set the initial variable value and then enter the
variable expression. Next, reenter to increment the variable and
calculate the square.

On the TI.89: On the TI.92 Plus: Display

0

§
2™
¸

NUM

2™
2Ë
¸

¸¸ ¸¸

NUM

j«1§

NUM

NUMZ2

§

0

NUM

¸

NUM«1
NUM

2Ë

NUMZ2

¸

§

Chapter 2: Operating the Calculator 49

r

Editing an entry lets

y

e

Tip:

ou make minor changes
without retyping the entire
entry.

Using the equation

2

, use trial and error to find the radius of a

A=pr

circle that covers 200 square centimeters.
The example below uses

as the first guess and then displays the

8

answer in its approximate floating-point form. You can edit and
reexecute using

and continue until the answer is as accurate as

7.95

you want.

On the TI.89: On the TI.92 Plus: Display

When the entry

Note:

contains a decimal point, th
result is automatically
displayed in floating-point.

Recalling a Previous
Entry

You can also use the

Note:

function to recall any

entry

previous entry. Refer to

in Appendix A.

entry()

2

8

2TRZ
¸

¥¸

A¥.

7.95

§R2Ë

2

¸

8

§jR2Ë

ãpä

2
¸

¥¸

A¥8

7.95

jRZ

¸

You can recall any previous entry that is stored in the history area,
even if the entry has scrolled off the top of the screen. The recalled

replaces

entry

whatever is currently shown on the entry line. You can

then reexecute or edit the recalled entry.

To recall: Press: Effect:

The last entry
(if you’ve changed
the entry line)

Previous entries

2²

once

2²

repeatedly

If the last entry is still shown on
the entry line, this recalls the
entry prior to that.

Each press recalls the entry prio
to the one shown on the entry
line.

For example:

If the entry line contains
the last entry, 2
recalls this entry.

If the entry line is edited
or cleared, 2
recalls this entry.

50 Chapter 2: Operating the Calculator

²

²

Recalling the Last
Answer

Each time you evaluate an expression, the
answer to the variable

2±

press

.

. To insert this variable in the entry line,

ans(1)

TI-89 / TI-92 Plus

stores the

For example, calculate the area of a garden plot that is 1.7 meters by

4.2 meters. Then calculate the yield per square meter if the plot
produces a total of 147 tomatoes.

1. Find the area.

p

4.2

¸

1.7

2. Find the yield.

e2±¸

147

Variable ans(1) is
inserted, and its value is
used in the calculation.

Refer to

Note:

Appendix A.

ans()

in

Just as

always contains the last answer,

ans(1)

also contain previous answers. For example,
next-to-last answer.

ans(2), ans(3)

contains the

ans(2)

, etc.,

Chapter 2: Operating the Calculator 51

I

R

v

p

Auto-Pasting an Entry or Answer from the History Area

You can select any entry or answer from the history area and
“auto-paste” a duplicate of it on the entry line. This lets you
insert a previous entry or answer into a new expression
without having to retype the previous information.

Why Use Auto-Paste

You can also paste

Note:

information by using the

toolbar menu. Refer to

ƒ

“Cutting, Copying, and
Pasting Information” in
Chapter 5.

Auto-Pasting an
Entry or Answer

To cancel auto-paste

Tip:

and return to the entry line,
press

N

.

The effect of using auto-paste is similar to

2²

and

2±

described in the previous section, but there are differences.

For entries:

For answers:

Pasting lets you:

nsert

any previous
entry into the entry
line.

Pasting lets you:

Insert the displayed

alue of

any

revious answer

into the entry line.

2²

eplace

lets you:

the contents of the
entry line with any previous
entry.

2±

Insert the variable
which contains

answer only

enter a calculation,

lets you:

the last

. Each time you

ans(1)

ans(1)

,

is

updated to the latest answer.

1. On the entry line, place the cursor where you want to insert the
entry or answer.

2. Press Cto move the cursor up into the history area. This
highlights the last answer.

3. Use Cand Dto highlight the entry or answer to auto-paste.

C

¦

moves from answer to
entry up through the history
area.

as

¦

To view an entry or

Tip:

answer too long for one line
(indicated by úat the end of
the line), use

and

2B

B

2A

and Aor

.

You can use Cto highlight
items that have scrolled off
the screen.

4. Press

¸

.

The highlighted item is inserted
in the entry line.

This pastes the entire entry or answer. If you need only a part of the
entry or answer, edit the entry line to delete the unwanted parts.

52 Chapter 2: Operating the Calculator

Status Line Indicators in the Display

The status line is displayed at the bottom of all application
screens. It shows information about the current state of the

, including several important mode settings.

Graph
Number

Angle

Mode

Exact/Approx

Mode

(G#1 on the
TI-92 Plus)

Shows the name of the current folder. Refer to
“Using Folders to Store Independent Sets of
Variables” in Chapter 5.
that is set up automatically when you use the

TI-89 / TI-92 Plus

Status Line
Indicators

TI-89 / TI-92 Plus

Current

Folder

Modifier

Key

Indicator Meaning

Current
Folder

Replace

Batteries

Graph

Mode

History Pairs,

Busy/Pause,

Locked Variable

is the default folder

MAIN

.

To cancel

Note:

, or

j

key again or press a
different modifier key.

Note:

press does not have a
diamond feature or an
associated letter, the key
performs its normal
operation.

¤

If the next key you

2, ¥

press the same

,

,

Modifier Key Shows which modifier key is in effect, as described

below.

2

2nd

— will use the second function of the next key

you press.

¥

2

— will use the diamond feature of the next key

you press.

j

(TI-89)

— will type the lowercase letter for the next

key you press.

(TI-89)

2 ™

— lowercase alpha-lock is on. Until you

turn this off, will type the lowercase letter for each

j

.

(TI-89)

key you press. To cancel alpha-lock, press

¤ j

— uppercase ALPHA-lock is on. Until you

turn this off, will type the uppercase letter for each

j

.

Angle
Mode

+

key you press. To cancel ALPHA-lock, press

¤

— will type the uppercase letter for the next key
you press. On the
letter without having to use

, you can use ¤ to type a

TI-89

j

.

Shows the units in which angle values are interpreted
and displayed. To change the

3

key.

mode, use the

Angle

RAD
DEG

Radians
Degrees

Chapter 2: Operating the Calculator 53

A

A

A

A

A

Œ

Status Line
(continued)

Indicator Meaning

Exact/

pprox

Mode

Shows how answers are calculated and displayed.
Refer to page 29. To change the
use the

3

key.

Exact/Approx

mode,

AUTO

EXACT

APPROX

Graph
Number

Graph
Mode

FUNC y(x)

PAR x(t)
POL r(q)

SEQ u(n)

3D z(x,y)

DE y'(t)

Battery

History Pairs,
Busy/Pause,

rchived

uto

Exact

pproximate

If the screen is split to show two independent graphs,
this indicates which graph is active —
(Displays

G#1

or

G#2

on the

TI-92 Plus

GR1

.)

or

GR2

.

Indicates the type of graphs that can be plotted. To
change the

mode, use the

Graph

3

key.

functions

and

parametric equations

y(t)

polar equations

sequences

3D equations

differential equations

Displayed only when the batteries are getting low. If

is shown with a black background, change the

BATT

batteries as soon as possible.

The information shown in this part of the status line
depends on the application you are using.

23/30

Displayed on the Home screen to show the number
of entry/answer pairs in the history area. Refer to
page 24.

BUSY

PAUSE

calculation or graph is in progress.
You paused a graph or program.
The variable opened in the current editor

(Data/Matrix Editor, Program Editor, or Text Editor)
is locked or archived and cannot be modified.

54 Chapter 2: Operating the Calculator

Finding the Software Version and ID Number

In some situations, you may need to find out information about
your

TI-89 / TI-92 Plus

unit’s ID number.

, particularly the software version and the

Displaying the
“About” Screen

When Do You Need
this Information?

From the Home screen, press

ƒ

and then select

Your screen will be different
than the one shown to the right.

¸

Press
screen.

The information on the
such as:

¦

If you obtain new or upgraded software for your
you may need to provide your current software version and/or the
ID number of your unit.

¦

If you have difficulties with your
contact technical support, knowing the software version may
make it easier to diagnose the problem.

or N to close the

A:About

.

screen is intended for situations

About

TI-89 / TI-92 Plus

TI-89 / TI-92 Plus

and need to

,

Chapter 2: Operating the Calculator 55

56 Chapter 2: Operating the Calculator

Chapter 3:
Symbolic Manipulation

Preview of Symbolic Manipulation........................................................ 58

Using Undefined or Defined Variables.................................................. 59

Using Exact, Approximate, and Auto Modes ....................................... 61

Automatic Simplification ........................................................................ 64

3

Delayed Simplification for Certain Built-In Functions ....................... 66

Substituting Values and Setting Constraints ........................................ 67

Overview of the Algebra Menu............................................................... 70

Common Algebraic Operations.............................................................. 72

Overview of the Calc Menu..................................................................... 75

Common Calculus Operations ............................................................... 76

User-Defined Functions and Symbolic Manipulation ......................... 77

If You Get an Out-of-Memory Error....................................................... 79

Special Constants Used in Symbolic Manipulation ............................. 80

This chapter is an overview of the fundamentals of using
symbolic manipulation to perform algebraic or calculus
operations.

You can easily perform symbolic calculations from the Home
screen.

Chapter 3: Symbolic Manipulation 57

g

Preview of Symbolic Manipulation

Solve the system of equations 2x ì3y = 4 and ëx + 7y = ë12. Solve the first equation so
that x is expressed in terms of y. Substitute the expression for x into the second equation,
and solve for the value of y. Then substitute the y value back into the first equation to
solve for the value of x.

Steps

1. Display the Home screen and
clear the entry line. Solve the
equation

2x ì3y = 4

„

1 selects

menu. You can also type
directly from the keyboard or select it
from the

for x.

solve(

Catalo

from the

.

Algebra

solve(

2. Begin to solve the equation

ë

x + 7y = ë12

¸

press

for y, but do not

yet.

3. Use the “with” operator to
substitute the expression for

x

that was calculated from the
first equation. This gives the
value of

The “with” operator is displayed as

on the screen.

Use the auto-paste feature to highlight

the last answer in the history area and
paste it to the entry line.

.

y

|

4. Highlight the equation for x in
the history area.

³

TI.89

Keystrokes

"
MM

1

„

2X|3YÁ4

bXd¸

1

„

·X«7YÁ

·12bYd

Í
C¸
¸

CCC

›

TI.92 Plus

Keystrokes Display

¥"
MM
„

1

2X|3YÁ4

d¸

X

1

„

·X«7YÁ

·12bYd

2Í
C¸
¸

CCC

b

5. Auto-paste the highlighted
expression to the entry line.
Then substitute the value of
that was calculated from the

y

¸
Í
C¸
¸

¸
2Í
C¸
¸

second equation.

The solution is:

x = ë8/11

and

y = ë20/11

This example is a demonstration of symbolic manipulation. A one-step function is available for
solving systems of equations. (See page 73.)

58 Chapter 3: Symbolic Manipulation

Using Undefined or Defined Variables

When performing algebraic or calculus operations, it is
important that you understand the effect of using undefined
and defined variables. Otherwise, you may get a number for a
result instead of the algebraic expression that you anticipated.

How Undefined and
Defined Variables
Are Treated

When defining a

Tip:

variable, it’s a good practice
to use more than one
character in the name.
Leave one-character names
undefined for symbolic
calculations.

When you enter an expression that contains a variable, the

TI-89 / TI-92 Plus

If the variable is

¦

treats the variable in one of two ways.

undefined, it is
treated as an
algebraic symbol.

If the variable is

¦

defined (even if
defined as 0), its value
replaces the variable.

To see why this is important, suppose you want to find the first
derivative of

If x is undefined, the

¦

ò

with respect to x.

x

result is in the form
you probably
expected.

If x is defined, the

¦

result may be in a
form you did not
expect.

Unless you knew that 5 had been
stored to x previously, the answer
75 could be misleading.

Determining If a
Variable Is
Undefined

Use

Note:

view a list of defined
variables, as described in
Chapter 21.

2°

Method: Example:

If defined, the variable’s
value is displayed.

Enter the variable
name.

to

Use the

getType

If undefined, the variable
name is displayed.

If defined, the variable’s
type is displayed.

function.

If undefined, “
displayed.

Chapter 3: Symbolic Manipulation 59

NONE

” is

v
A

Deleting a Defined
Variable

You can “undefine” a defined variable by deleting it.

To delete: Do this:

One or more specified

Use the

DelVar

function.

ariables

You can also delete variables by using the

VAR-LINK

screen (

2°

described in Chapter 21.

) as

For information about

Note:

folders, refer to Chapter 5.

Temporarily
Overriding a
Variable

For more information

Note:

about the
page 67.

operator, refer to

|

ll one-letter variables

(

– z) in the current

a

folder

From the Home screen
select 1:
press

Clear a-z

¸

to confirm the deletion.

By using the “with” operator ( | ), you can:

Temporarily override

¦

a variable’s defined
value.

Temporarily define a

¦

value for an undefined
variable.

To type the “with” operator ( | ), press:

Í

TI.89:
TI.92 Plus:

2

Í

Clean Up

menu,

. You will be prompted to

60 Chapter 3: Symbolic Manipulation

∫

A

Using Exact, Approximate, and Auto Modes

The Exact/Approx mode settings, which are described briefly
in Chapter 2, directly affect the precision and accuracy with
which the

TI-89 / TI-92 Plus

describes these mode settings as they relate to symbolic
manipulation.

calculates a result. This section

EXACT

Setting

When

Exact/Approx = EXACT

, the

TI-89 / TI-92 Plus

uses exact rational

arithmetic with up to 614 digits in the numerator and 614 digits in the

and

3

setting:

ln(1000)

transforms to

.

1/4

3 ln(10)

fMin

,

12

.

, and

fMax

denominator. The

Transforms irrational numbers to standard forms as much as

¦

EXACT

possible without approximating them. For example,
transforms to

Converts floating-point numbers to rational numbers. For

¦

example,

The functions

2

transforms to

0.25

solve, cSolve, zeros, cZeros, factor,

use only exact symbolic algorithms. These functions do not compute
approximate solutions in the

Some equations, such as

¦

EXACT

2–x = x

setting.

, have solutions that cannot all be

finitely represented in terms of the functions and operators on the

TI-89 / TI-92 Plus

With this kind of equation,

¦

solutions. For example,

x ≈ 0.641186

Advantages Disadvantages

Results are exact.

.

EXACT

2–x = x

will not compute approximate

has an approximate solution

, but it is not displayed in the

s you use more complicated rational

EXACT

setting.

numbers and irrational constants,
calculations can:

Use more memory, which may

¦

exhaust the memory before a solution
is completed.

Take more computing time.

¦

Produce bulky results that are harder

¦

to comprehend than a floating-point
number.

Chapter 3: Symbolic Manipulation 61

∫

A

A

APPROXIMATE

Setting

When

Exact/Approx = APPROXIMATE

, the

TI-89 / TI-92 Plus

converts
rational numbers and irrational constants to floating-point. However,
there are exceptions:

Certain built-in functions that expect one of their arguments to be

¦

an integer will convert that number to an integer if possible. For
example:

Whole-number floating-point exponents are converted to integers.

¦

For example:

d

(y(x), x, 2.0)

2.0

transforms to

x

transforms to

d

(y(x), x, 2)

2

even in the

x

.

APPROXIMATE

setting.

Functions such as

solve

and

(integrate)

can use both exact symbolic
and approximate numeric techniques. These functions skip all or
some of their exact symbolic techniques in the

APPROXIMATE

setting.

Advantages Disadvantages

If exact results are not
needed, this might save
time and/or use less
memory than the

EXACT

setting.

pproximate results are
sometimes more
compact and
comprehensible than
exact results.

If you do not plan to use
symbolic computations,
approximate results are

Results with undefined variables or
functions often exhibit incomplete
cancellation. For example, a coefficient
that should be
small magnitude such as

might be displayed as a

0

1.23457E-11

Symbolic operations such as limits and
integration are less likely to give
satisfying results in the

APPROXIMATE

setting.

pproximate results are sometimes less
compact and comprehensible than exact
results. For example, you may prefer to
see

instead of

1/7

.142857

.
similar to familiar,
traditional numeric
calculators.

.

62 Chapter 3: Symbolic Manipulation

AUTO

Setting

When

Exact/Approx = AUTO

, the

TI-89 / TI-92 Plus

uses exact rational
arithmetic wherever all of the operands are rational numbers.
Otherwise, floating-point arithmetic is used after converting any
rational operands to floating-point. In other words, floating-point is
“infectious.” For example:

1/2 − 1/3

transforms to

1/6

but

0.5 − 1/3

transforms to

.16666666666667

This floating-point infection does not leap over barriers such as
undefined variables or between elements of lists or matrices. For
example:

(1/2 - 1/3) x + (0.5 − 1/3) y

transforms to

x/6 + .16666666666667 y

and

{1/2 - 1/3, 0.5 − 1/3}

In the

setting, functions such as

AUTO

transforms to

{1/6, .16666666666667}

solve

determine as many
solutions as possible exactly, and then use approximate numerical
methods if necessary to determine additional solutions. Similarly,

‰

(integrate)

uses approximate numerical methods if appropriate

where exact symbolic methods fail.

Advantages Disadvantages

You see exact results
when practical, and
approximate numeric
results when exact
results are impractical.

You can often control
the format of a result by
choosing to enter some

If you are interested only in exact results,
some time may be wasted seeking
approximate results.

If you are interested only in approximate
results, some time may be wasted
seeking exact results. Moreover, you
might exhaust the memory seeking those

exact results.
coefficients as either
rational or floating-point
numbers.

Chapter 3: Symbolic Manipulation 63

Automatic Simplification

When you type an expression on the entry line and press

¸

, the

expression according to its default simplification rules.

TI-89 / TI-92 Plus

automatically simplifies the

Default
Simplification Rules

For information about

Note:

folders, refer to Chapter 5.

Refer to “Delayed

Note:

Simplification for Certain
Built-In Functions” on
page 66.

All of the following rules are applied automatically. You do not see
intermediate results.

¦

If a variable has a defined value, that value replaces the variable.

If the variable is defined in terms
of another variable, the variable
is replaced with its “lowest level”
value (called infinite lookup).

Default simplification does not modify variables that use path
names to indicate a folder. For example,
simplify to

¦

For functions:

−

The arguments are simplified. (Some built-in functions delay

2x

.

x+class\x

does not

simplification of some of their arguments.)

−

If the function is a built-in or user-defined function, the
function definition is applied to the simplified arguments.
Then the functional form is replaced with this result.

¦

Numeric subexpressions are
combined.

¦

Products and sums are sorted
into order.

Products and sums involving undefined variables are sorted
according to the first letter of the variable name.

−

Undefined variables
variables, and are placed in alphabetical order at the beginning
of a sum.

−

Undefined variables
constants, and are placed in alphabetical order at the end of a
sum (but before numbers).

¦

Similar factors and similar terms
are collected.

64 Chapter 3: Symbolic Manipulation

through z are assumed to be true

r

through q are assumed to represent

a

This floating-point number
causes numeric results to be
shown as floating-point.

If a floating-point whole
number is entered as an
exponent, it is treated as
an integer (and does not
produce a floating-point
result).

¦

Identities involving zeros and ones
are exploited.

¦

Polynomial greatest common
divisors are canceled.

¦

Polynomials are expanded unless
no key cancellation can occur.

¦

Common denominators are
formed unless no key cancellation
can occur.

No key cancellation

How Long Is the
Simplification
Process?

No key cancellation

¦

Functional identities are
exploited. For example:

ln(2x) = ln(2) + ln(x)

and

sin(x)ñ+ cos(x)ñ= 1

Depending on the complexity of an entry, result, or intermediate
expression, it can take a long time to expand an expression and
cancel common divisors as necessary for simplification.

To interrupt a simplification process that is taking too long,
press ´. You can then try simplifying only a portion of the
expression. (Auto-paste the entire expression on the entry line, and
then delete the unwanted parts.)

Chapter 3: Symbolic Manipulation 65

Delayed Simplification for Certain Built-In Functions

Usually, variables are automatically simplified to their lowest
possible level before they are passed to a function. For certain
functions, however, complete simplification is delayed until
after the function is performed.

Functions that Use
Delayed
Simplification

Not all functions that

Note:

use a var argument use
delayed simplification.

You may or may not

Note:

want to define a numeric
value for var, depending on
the situation.

Functions that use delayed simplification have a required

var

argument that performs the function with respect to a variable.
These functions have at least two arguments with the general form:

function

expression, var

(

For example:

solve

d

‰

(x^2ìxì2,x)

limit

(x^2

(x

(x^2

ìxì

ñ

[, ... ]

ìxì

ìxì

)

2=0,x)

2,x)

2,x,5)

For a function that uses delayed simplification:

1. The

var

variable is simplified to the lowest level at which it
remains a variable (even if it could be further simplified to a
non-variable value).

2. The function is performed using the variable.

var

3. If

can be further simplified, that value is then substituted into

the result.

For example:

x cannot be simplified.

The example to the

Note:

right finds the derivative of
xòat x=5. If xòwas initially
simplified to 75, you would
find the derivative of 75,
which is not what you want.

66 Chapter 3: Symbolic Manipulation

x is not simplified. The
function uses xò, and
then substitutes 5 for x.

x is simplified to t. The
function uses tò.

x is simplified to t. The
function uses tò, and
then substitutes 5 for t.

v

v

v

v

Substituting Values and Setting Constraints

The “with” operator ( | ) lets you temporarily substitute values
into an expression or specify domain constraints.

Typing the “With”
Operator

Substituting for a
Variable

Substituting for a
Simple Expression

To type the “with” operator ( | ), press:

Í

TI.89:
TI.92 Plus:

2

Í

For every occurrence of a
specified variable, you can
substitute a numeric value or an
expression.

To substitute for multiple

ariables at the same time, use

the Boolean

and

operator.

For every occurrence of a simple
expression, you can substitute a

ariable, numeric value, or

another expression.

First derivative of xìò at x = 5

Substituting s for sin(x) shows that
the expression is a polynomial in
terms of sin(x).

from

acos(x)

a*cos(x)

.

By replacing a commonly used
(or long) term, you can display

is different

Note:

results in a more compact form.

Substituting
Complex Values

You can substitute complex

alues just as you would for other
alues.

For an overview of

Note:

complex numbers, refer to
Appendix B.

To get the complex

Tip:

press
type the letter i on the
keyboard.

2)

Do not simply

.

All undefined variables are treated as real numbers in symbolic
calculations. To perform complex symbolic analysis, you must define
a complex variable. For example:

,

i

x+y

i

!

z

Then you can use z as a complex variable. You can also use z_. For
more information see the _ (underscore) topic in Appendix A.

Chapter 3: Symbolic Manipulation 67

Be Aware of the
Limitations of
Substitutions

¦

Substitution occurs only
where there is an

exact

Only x2 was replaced, not x4.

match for the substitution.

Define the substitution in
simpler terms for a more
complete substitution.

¦

Infinite recursions can occur when you define a substitution
variable in terms of itself.

Substitutes sin(x+1), sin(x+1+1), sin(x+1+1+1), etc.

sin(x)|x=x+1

When you enter a substitution that causes an infinite recursion:

−

An error message is
displayed.

−

When you press N, an
error is shown in the
history area.

Use the

Tip:

to help determine the single­variable substitution.

solve

function

¦

Internally, an expression is sorted according to the automatic
simplification rules. Therefore, products and sums may not match
the order in which you entered them.

−

As a general rule, you
should substitute for a
single variable.

−

Substituting for more

No match for substitution

general expressions
(either
or

møcñ=e

cñøm=e

) may not work

as you anticipate.

68 Chapter 3: Symbolic Manipulation

Specifying Domain

f

Constraints

ln(xùy)

or

2¿

instead o

¥Ã

2

Enter

Tip:

; otherwise, xy is

ln(xy)

interpreted as a single
variable named xy.

For ‚ or , press

Tip:

or ¥Â. You can also use

2I

select them from a menu.

8

Many identities and transformations are valid for only a particular
domain. For example:

ln(xùy) = ln(x) + ln(y)
sinê(sin(q)) =

q

only if x and/or y is not negative

ë

only if q ‚

p

and q 

/2

p

radians

/2

Use the “with” operator to specify the domain constraint.

Because ln(xùy) = ln(x) + ln(y) is not always
valid, the logarithms are not combined.

With a constraint, the identity is valid
and the expression is simplified.

Because sinê(sin(q)) = q is not always
valid, the expression is not simplified.

to

With a constraint, the expression can
be simplified.

Using Substitutions
vs. Defining a
Variable

Caution:

it can affect all calculations
that involve x (until you
delete x).

After x is defined,

In many cases, you can
achieve the same effect
as a substitution by
defining the variable.

However, substitution is preferable for most cases because the
variable is defined only for the current calculation and does not
accidentally affect later calculations.

Substituting x=1 does
not affect the next
calculation.

Storing 1!x affects
the subsequent
calculations.

Chapter 3: Symbolic Manipulation 69

v

v
v

v

Overview of the Algebra Menu

The Algebra Menu

For a complete

Note:

description of each function
and its syntax, refer to
Appendix A.

You can use the „

Algebra

toolbar menu to select the most

commonly used algebraic functions.

From the Home screen, press „ to display:

This menu is also available from the
menu. Press

9:Algebra

Menu Item Description

solve

Solves an expression for a specified variable. This

2I

.

returns real solutions only, regardless of the

mode setting. Displays answers with

A:Complex

factor

Complex Format

" and "or" connecting solutions. (For complex

"

and

solutions, select

Factors an expression with respect to all its

ariables or with respect to only a specified
ariable.

and then select

from the

Algebra

MATH

menu.)

expand

zeros

approx

comDenom

propFrac

nSolve

Expands an expression with respect to all its

ariables or with respect to only a specified
ariable.

Determines the values of a specified variable that
make an expression equal to zero. Displays in a list.

Evaluates an expression using floating-point
arithmetic, where possible. This is equivalent to

3

using
(or using

to set

¥¸

Exact/Approx = APPROXIMATE

to evaluate an expression).

Calculates a common denominator for all terms in
an expression and transforms the expression into a
reduced ratio of a numerator and denominator.

Returns an expression as a proper fraction
expression.

Calculates a single solution for an equation as a
floating-point number (as opposed to

solve

, which
may display several solutions in a rational or
symbolic form).

70 Chapter 3: Symbolic Manipulation

Menu Item Description

Trig

Displays the submenu:

left

and

right

The

Note:

functions are also used to
return a specified number of
elements or characters from
the left or right side of a list
or character string.

Complex

Extract

tExpand

Expands trig expressions with angle sums
and multiple angles.

tCollect

Collects the products of integer powers of
trig functions into angle sums and
multiple angles.

tExpand

.

tCollect

Displays the submenu:

These are the same as

solve, factor

they also compute complex results.

Displays the submenu:

getNum

Applies

comDenom

and then returns the

resulting numerator.

getDenom

Applies

comDenom

and then returns the

resulting denominator.

left

Returns the left-hand side of an equation
or inequality.

right

Returns the right-hand side of an equation
or inequality.

is the opposite of

zeros

, and

; but

Chapter 3: Symbolic Manipulation 71

p

p

v

Common Algebraic Operations

This section gives examples for some of the functions
available from the
information about any function, refer to Appendix A. Some
algebraic operations do not require a special function.

„

Algebra

toolbar menu. For complete

Adding or Dividing
Polynomials

Factoring and
Expanding
Polynomials

Finding Prime
Factors of a Number

You can add or divide

olynomials directly, without

using a special function.

Use the

factor

expand

Factor

factor

x

„

(

) and

2

expression [,var

(

expression [,var

(

5

ì

. Then expand the

1

expand

])

for factoring with respect to a variable

])

for partial expansion with respect to a variable

result.

Notice that

factor

and

expand

erform opposite operations.

The

factor

„

(

) function lets you do more than simply factor an

2

algebraic polynomial.

You can find prime factors of a
rational number (either an integer
or a ratio of integers).

„

(

) functions.

3

Finding Partial
Expansions

With the

expand

„

(

) function’s optional

3

partial expansion that collects similar powers of a variable.

Do a full expansion of

(yñìy)

with respect to all

(xñìx)

var

value, you can do a

ariables.

Then do a partial expansion with
respect to

72 Chapter 3: Symbolic Manipulation

.

x

Solving an Equation

Use the

solve

variable.

solve

(

Solve

x + y ì5 = 2x ì5y

for x.

„

(

) function to solve an equation for a specified

1

equation, var

)

An operation such as

Note:

subtracts 2x from

2

|

Ù

both sides.

Solving a System of
Linear Equations

simult

menu. Use

or the

and

rref

Catalog.

The

Note:

matrix functions are not on
the

Algebra

„

2I

4

Notice that

solve

displays

only the final result.

To see intermediate results, you can manually solve the equation
step-by-step.

x « y | 5 Á 2x | 5y

|

2 x

|

y

«

5

p ·

1

Consider a set of two equations with
two unknowns:

2x ì3y = 4

ë

x + 7y = ë12

To solve this system of equations, use any of the following methods.

Method Example

Use the

solve

function

solve

2xì3y=4 and ëx+7y=ë12,{x,y}

(

)

for a one-step solution.

Use the

solve

function
with substitution ( | )
for step-by-step

Refer to the preview at the beginning of
this chapter, which solved for
and

y = ë20/11

.

x = ë8/11

manipulation.

Use the
with a matrix.

simult

function

Enter the coefficients as a matrix and the
results as a constant column matrix.

Use the

rref

function

with a matrix.

Enter the coefficients as an augmented
matrix.

Chapter 3: Symbolic Manipulation 73

Finding the Zeros of

r

an Expression

Use the

zeros

zeros

„

(

4

expression, var

(

) function.

)

For ‚ or , type

Tip:

.You can also use

¥ Â
2I

select them from a menu.

or

8

¥ Ã

2¿

2

Finding Proper
Fractions and
Common
Denominators

You can use

Note:

comDenom

expression, list, or matrix.

with an

o

Use the expression

x ùsin(x) + cos(x)

to

.

Find the zeros with respect to
in the interval

Use the

propFrac

comDenom

0  x

propFrac

(

rational expression [,var

(

expression [,var

(

Find a proper fraction for the
expression

4

ì2xñ

(x

+ x) / (2xñ+ x + 4)

Then transform the answer into
a ratio of a fully expanded
numerator and a fully expanded
denominator.

Notice that

comDenom

propFrac

perform opposite

operations.

In this example:

and

„

and

x  3

) and

7

x

.

Use the “with”
operator to specify
the interval.

comDenom

])

for common denominators that collect

for common denominators that collect
similar powers of this variable

similar powers of this variable

„

(

) functions.

6

])

for proper fractions with respect
to a variable

.

If you do this example on your
TI-89 / TI-92 Plus, the
function scrolls off the top of the
screen.

propFrac

31 x + 60

¦

¦

74 Chapter 3: Symbolic Manipulation

8

ñ

x

x

ì

ì

4

2

is the remainder of

is the quotient.

15/8

4

x

ì2xñ

divided by

+x

2xñ+x+4

.

‰

v

Overview of the Calc Menu

s

The Calc Menu

For a complete

Note:

description of each function
and its syntax, refer to
Appendix A.

symbol for

The

Note:

differentiate is a special
symbol. It is not the same a
typing
keyboard. Use

2 =

d

the letter D

…

.

on the

or

1

You can use the …

Calc

toolbar menu to select commonly

used calculus functions.

From the Home screen, press … to display:

This menu is also available from the
menu. Press

A:Calculus

Menu Item Description

d

differentiate

Differentiates an expression with respect to a

2I

.

specified variable.

integrate

Integrates an expression with respect to a specified

ariable.

limit

Calculates the limit of an expression with respect to
a specified variable.

G

sum

Evaluates an expression at discrete variable values
within a range and then calculates the sum.

MATH

and then select

Π

product

fMin

fMax

arcLen

taylor

nDeriv

nInt

deSolve

Evaluates an expression at discrete variable values
within a range and then calculates the product.

Finds candidate values of a specified variable that
minimize an expression.

Finds candidate values of a specified variable that
maximize an expression.

Returns the arc length of an expression with respect
to a specified variable.

Calculates a Taylor polynomial approximation to an
expression with respect to a specified variable.

Calculates the numerical derivative of an expression
with respect to a specified variable.

Calculates an integral as a floating-point number
using quadrature (an approximation using weighted
sums of integrand values).

Symbolically solves many 1st and 2nd order
differential equations, with or without initial
conditions.

Chapter 3: Symbolic Manipulation 75

p

p

Common Calculus Operations

This section gives examples for some of the functions
available from the …
information about any calculus function, refer to Appendix A.

Calc

toolbar menu. For complete

Integrating and
Differentiating

You can integrate an

Note:

expression only; you can
differentiate an expression,
list, or matrix.

Finding a Limit

You can find a limit

Note:

for an expression, list, or
matrix.

Use the

‰

expression, var

(

expression, var

d

(

Integrate
to

.

x

‰

integrate

xñùsin(x)

…

(

) and

2

low

[,

] [,up])

order

[,

])

with respect

Differentiate the answer with
respect to

Use the

limit

Find the limit of

.

x

…

limit

(

) function.

3

expression, var, point

(

sin(3x) / x

as

approaches 0.

d

differentiate

lets you specify limits or a
constant of integration

direction

[,

x

…

(

To get d, use … 1 or 2 =. Do
not simply type the letter D on
the keyboard.

])*

negative = from left
positive = from right
omitted or 0 = both

) functions.

1

Finding a Taylor
Polynomial

Important:

scaling by p/180 may cause
calculus application results
to appear in a different form.

Degree-mode

Use the

taylor

taylor

Find a 6th order Taylor

olynomial for

respect to

…

(

) function.

9

expression, var, order

(

with

sin(x)

.

x

[,

point

])

if omitted, expansion point is 0

Store the answer as a user­defined function named

Then graph

and the Taylor

sin(x)

y1(x)

.

Graph sin(x):Graph y1(x)

olynomial.

76 Chapter 3: Symbolic Manipulation

User-Defined Functions and Symbolic Manipulation

You can use a user-defined function as an argument for the

TI-89 / TI-92 Plus’s

built-in algebra and calculus functions.

For Information
about Creating a
User-Defined
Function

Undefined
Functions

To select

Tip:

toolbar menu, press

Calc

(or press

1

…

keyboard).

from the

d

2 =

on the

Single-Statement
Functions

Refer to:

¦

“Creating and Evaluating User-Defined Functions” in Chapter 5.

¦

“Graphing a Function Defined on the Home Screen” and
“Graphing a Piecewise Defined Function” in Chapter 12.

¦

“Overview of Entering a Function” in Chapter 17.

You can use functions such as

f(x), g(t), r(q)

, etc., that have not been
assigned a definition. These “undefined” functions yield symbolic
results. For example:

DelVar

Use
and

to ensure that

are not defined.

g(x)

f(x)

Then find the derivative of

f(x)ùg(x)

with respect to x.

You can use user-defined functions consisting of a single expression.
For example:

¦

§

Use

sec(x) =

to create a user-defined secant function, where:

1

cos(x)

To select

Tip:

toolbar menu, press

Calc

.

3

…

To select ‰ from the

Tip:

toolbar menu, press

Calc

(or press

2

…

keyboard). To select
press

…

9.

limit

2 <

from the

on the

taylor

Then find the limit of
as x approaches

¦

,

Define

Use

h(x)=

to create a user-defined function

x

⌠

sin(t) / t

⌡

0

Then find a 5th order Taylor
polynomial for
respect to

.

x

p

h(x)

.

/4

with

sec(x)

, where:

h(x)

Define h(x)= ‰(sin(t)/t,t,0,x).

Chapter 3: Symbolic Manipulation 77

Multi-Statement vs.
Single-Statement
Functions

You can use your

Tip:

computer keyboard to type
lengthy text and then use

TI-GRAPH LINK to

the

TI-89 / TI 92-Plus.

Chapter 18 for more
information.

send it to

See

Multi-statement user-defined functions should be used as an
argument for numeric functions (such as

nDeriv

and

nInt

) only.

In some cases, you may be able to create an equivalent single­statement function. For example, consider a piecewise function with
two pieces.

When: Use expression:

x < 0
x ‚ 0 5 cos(x)

If you were to create a multi-statement user-defined function with

¦

ë

x

the form:

Func
If x<0 Then
Return ëx
Else
Return 5cos(x)
EndIf
EndFunc

Define y1(x)=Func:If x<0 Then: ... :EndFunc

To select

Tip:

toolbar menu, press

Calc

B:nInt.

…

To select

Tip:

toolbar menu, press

Calc

(or press

2

…

keyboard).

from the

nInt

‰

from the

2 <

on the

Then numerically
integrate
respect to

Create an equivalent single-statement user-defined function.

¦

Use the

TI-89 / TI-92 Plus’s

built-in

y1(x)

x

when

with

.

Define y1(x)=when(x<0,ëx, 5cos(x))

function.

Then integrate

y1(x)

with respect to x.

Press ¥
floating-point result.

¸

for a

78 Chapter 3: Symbolic Manipulation

If You Get an Out-of-Memory Error

Freeing Up Memory

Simplifying
Problems

The

TI-89 / TI-92 Plus

stores intermediate results in memory and
then deletes them when the calculation is complete. Depending
on the complexity of the calculation, the

TI-89 / TI-92 Plus

may run

out of memory before a result can be calculated.

¦

Delete unneeded variables and/or Flash applications, particularly
large-sized ones.

−

2°

Use

as described in Chapter 21 to view and

delete variables and/or Flash applications.

¦

On the Home screen:

−

Clear the history area (ƒ

−

You can also use ƒ

) or delete unneeded history pairs.

8

to reduce the number of history pairs

9

that will be saved.

¦

3

Use

to set

Exact/Approx = APPROXIMATE

. (For results that have

a large number of digits, this uses less memory than

AUTO

or

For results that have only a few digits, this uses more memory.)

¦

Split the problem into parts.

−

Split

solve

(aùb=0,

var

into

)

solve

(a=0,

var

and

)

solve

(b=0,

Solve each part and combine the results.

EXACT

var

)

.

.

¦

If several undefined variables occur only in a certain
combination, replace that combination with a single variable.

−

If

and c occur only as

m

(a+b)ñ+ (a+b)

−

In the expression

1 ìc

ñ

. In the solution, replace c with

ñ

cñ+ c

use

¦

For expressions combined over a common denominator, replace

ñ

mùc

1 ì(a+b)

, substitute e for

ñ

, substitute c for

ñ

mùc

(a+b)

ñ

.

.

(a+b)

sums in denominators with unique new undefined variables.

−

In the expression

añ+bñ + c
añ+bñ + c

¦

Substitute known numeric values for undefined variables at an

and use

.

x

añ+bñ + c

x

+

d

+

y

. In the solution, replace d with

d

y

añ+bñ + c

, substitute d for

earlier stage, particularly if they are simple integers or fractions.

¦

Reformulate a problem to avoid fractional powers.

¦

Omit relatively small terms to find an approximation.

and

Chapter 3: Symbolic Manipulation 79

Special Constants Used in Symbolic Manipulation

The result of a calculation may include one of the special
constants described in this section. In some cases, you may
also need to enter a constant as part of your entry.

x=x is true for any value of x.

true, false

n1 ... @n255

@

For @, press:

¥§

TI.89

:

e

¥ *

:

¥ s

2

:

2 *

2 s

TI.92 Plus

,

ˆ

For ˆ, press:

TI.89
TI.92 Plus:

For e, press:

TI.89:
TI.92 Plus:

R

These indicate the result
of an identity or a
Boolean expression.

This notation indicates
an “arbitrary integer”
that represents any
integer.

When an arbitrary
integer occurs multiple
times in the same
session, each
occurrence is numbered
consecutively. After it
reaches 255, arbitrary
integer consecutive
numbering restarts at
@n0. Use

2:NewProb
@n1

ˆ

represents infinity,

Clean Up

to reset to

.

and e represents the
constant

2.71828...

(base of the natural
logarithms).

These constants are
often used in entries as
well as results.

5<3 is false.

A solution is at every integer
multiple of p.

Both @n1 and @n2 represent
any arbitrary integer, but this
notation identifies separate
arbitrary integers.

undef

80 Chapter 3: Symbolic Manipulation

This indicates that the result is undefined.

Mathematically undefined

„ˆ

(undetermined sign)

Non-unique limit

Chapter 4:
Constants and Measurement Units

Preview of Constants and Measurement Units.................................... 82

Entering Constants or Units ................................................................... 83

Converting from One Unit to Another................................................... 85

4

Setting the Default Units for Displayed Results................................... 87

Creating Your Own User-Defined Units................................................ 88

List of Pre-Defined Constants and Units............................................... 89

Constant and unit

Note:

names always begin with an
underscore

Note:

getUnits()

default units or
set the default units. Refer
to Appendix A.

.

_

You can also use

to get a list of the

setUnits()

to

The
units from different categories.

Page 3

systems of measurement to specify the default units for displayed
results.

By using the unit features, you can:

dialog box lets you select the available constants or

UNITS

This category lists

constant values.

Remaining categories

list available units.

…

(

) of the

dialog box lets you select from three

MODE

International system of
measurements (metric or
MKS) – meters, kilograms, etc.

English system – feet,
pounds, etc.

Lets you select the units you
want to use.

¦

Enter a unit for values in an expression, such as 6_m ù4_m or
23_m/_s ù10_s. The result is displayed in the selected default
units.

¦

Convert values from one unit to another within the same
category.

¦

Create your own user-defined units. These can be a
combination of existing units or unique “standalone” units.

Chapter 4: Constants and Measurement Units 81

g

g

Preview of Constants and Measurement Units

Using the equation f = mùa, calculate the force when m = 5 kilograms and a = 20
meters/secondñ. What is the force when a = 9.8 meters/secondñ. (This is the
acceleration due to gravity, which is a constant named _g). Convert the result from
newtons to kilograms of force.

Steps

1. Display the
. For

Page 3

select

for the metric system of

SI

dialog box,

MODE
Unit System

mode,

measurements.

Results are displayed according to

these default units.

Create

2.

The UNITS dialog box lets you select

Now, instead of re-entering

Also, you can now use the UNITS

an acceleration unit for

meters/second

units from an alphabetical list of
categories. You can use

2C

to scroll one page at a time

through the categories.

each time you need it, you can use

.

_ms2

dialog box to select

Acceleration

2

named _ms2.

_ms2

category.

2D

and

_m/_s

from the

ñ

3. Calculate the force when

m = 5 kilograms (_kg) and
a = 20 meters/second

If you know the abbreviation for a unit,

you can type it from the keyboard.

2

(_ms2).

³

TI-89

Keystrokes

3…B

1

¸

29DB
¸
e29
DDDB

S

¸
Z2§
¥
2™

MS

j2¸

5

¥
2™
jp

KG

20

¥2™

MS

j

2

¸

›

TI-92 Plus

Keystrokes Display

B

3…

1

¸

¥

M

9

DB

M

¸
e¥9

DDDB

S

¸
Z2§

2



MS
2

¸

2

5



KG

20

p

2



MS2

¸

If you use the UNITS
dialog box to select a
unit, the _ is entered
automatically.

4. Using the same m, calculate the
force for an acceleration due to
gravity (the constant _g).

For

, you can use the pre-defined

_

constant available from the UNITS
dialog box or you can type

.

_

5. Convert to kilograms of force
(_kgf).

2

82 Chapter 4: Constants and Measurement Units

displays the 4 conversion

operator.

5

¥

2™

KG

jp
29B

G

j
¸¸

B2¥
2™

KGF

j¸

5

2

KG

p

¥

9

B

G

¸¸

B

22

KGF

¸

Entering Constants or Units

You can use a menu to select from a list of available constants
and units, or you can type them directly from the keyboard.

From a Menu

2D

and

2C

Use

Tip:

to scroll one page at a time
through the categories.

If you created a user-

Note:

defined unit for an existing
category (page 88), it is
listed in the menu.

The following shows how to select a unit, but you can use the same
general procedure to select a constant.

From the Home screen:

1. Type the value or expression.

2. Display the

UNITS

dialog box.

6.3

Press:

2 À

TI.89:
TI.92 Plus:

¥ 9

3. Use D and C to move the cursor
to the applicable category.

4. To select the highlighted (default)
unit, press

¸

.
– or –
To select a different unit from the
category, press B. Then highlight
the applicable unit, and press

¸

.

You can also move the cursor

The selected unit is placed in the
entry line. Constant and unit names
always begin with an underscore (

_

by typing the first letter of a

6.3_pF

).

unit.

From the Keyboard

You can type units in

Note:

either uppercase or
lowercase characters.

If you know the abbreviation that the

TI-89 / TI-92 Plus

uses for a
particular constant or unit (refer to the list that begins on page 89),
you can type it directly from the keyboard. For example:

256_m

The first character must be an underscore ( _ ). For _, press:

¥



2



256_m, 256 _m

ù

) before the underscore is
, and

256ù_m

are

TI.89:
TI.92 Plus:

A space or a multiplication symbol (

¦

optional. For example,
equivalent.

−

However, if you are adding units to a variable, you must put a
space or ùbefore the underscore. For example,
as a variable, not as

Chapter 4: Constants and Measurement Units 83

with a unit.

x

is treated

x_m