Texas Instruments TI-86 User Manual

TI-86

GRAPHING CALCULATOR

GUIDEBOOK

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Important

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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.

iii

TI-86 Quick Start 1

Preparing to Use Your New TI-86 ..................................................... 2

Installing the AAA Batteries ......................................................... 2

Turning On and Turning Off the TI-86.......................................... 2

Adjusting the Contrast .................................................................2

Resetting All Memory and Defaults.............................................. 3

Calculating on the Home Screen.......................................................3

Calculating the Sine of a Number.................................................3

Storing the Last Answer to a Variable..........................................3

Using a Variable in an Expression ................................................4

Editing an Expression ................................................................... 4

Displaying a Complex Number as a Result...................................5

Using a List with a Function......................................................... 5

Displaying the Integer Part of Real Numbers in a List .................. 6

Removing (Exiting) a Menu..........................................................6

Finding the Square Root............................................................... 7

Calculating Derivatives................................................................. 7

Retrieving, Editing, and Re-evaluating the Previous Entry ...........8

Converting Degrees Fahrenheit to Degrees Celsius...................... 8

Storing an Unevaluated Expression to an Equation Variable .......9

Plotting Functions on the Graph Screen............................................ 9

Displaying and Entering Functions in the Equation Editor............9

Changing the Graph Style of a Function.....................................10

Plotting a Function on the Graph Screen....................................11

Tracing a Function......................................................................11

Evaluating y for a Specific x Value (During a Trace) ................... 12

Changing a Window Variable Value........................................... 12

Deselecting a Function ...............................................................13

Zooming In on a Portion of the Graph Screen ............................ 14

Chapter 1: Operating the TI-86 15

Installing or Replacing Batteries .....................................................16

When to Replace Batteries .........................................................16

Turning On and Turning Off the TI-86.............................................17

Adjusting the Display Contrast........................................................17

The Home Screen ............................................................................18

Displaying Entries and Answers..................................................18

Entering Numbers ...........................................................................19

Entering Negative Numbers .......................................................19

Using Scientific or Engineering Notation....................................20

Entering Complex Numbers........................................................ 20

Entering Other Characters............................................................... 21

The 2nd Key................................................................................21

TI-86 Table of Contents

The ALPHA Key........................................................................... 21

ALPHA-lock and alpha-lock........................................................ 22

Common Cursors........................................................................ 22

Cursor Direction Keys ................................................................. 23

Inserting, Deleting, and Clearing Characters..............................23

Entering Expressions and Instructions ............................................24

Entering an Expression...............................................................24

Using Functions in Expressions ..................................................25

Using an Instruction ................................................................... 25

Entering Functions, Instructions, and Operators ........................25

Entering Consecutive Entries...................................................... 26

The Busy Indicator...................................................................... 26

Interrupting a Calculation or Graph ...........................................26

Diagnosing an Error ........................................................................ 27

Correcting an Error..................................................................... 27

Reusing Previous Entries and the Last Answer ...............................28

Retrieving the Last Entry ............................................................ 28

Retrieving and Editing the Last Entry .........................................28

Retrieving Previous Entries......................................................... 28

Retrieving Multiple Entries......................................................... 29

Clearing the ENTRY Storage Area ..............................................29

Retrieving the Last Answer ........................................................29

Using Ans Preceding a Function.................................................30

Storing Results to a Variable ...................................................... 30

Using TI-86 Menus..........................................................................31

Displaying a Menu......................................................................31

The Menu Keys...........................................................................32

Selecting a Menu Item................................................................32

Exiting (Removing) a Menu ........................................................33

Viewing and Changing Modes ........................................................34

Changing a Mode Setting...........................................................34

Chapter 2: The CATALOG, Variables, and Characters 37

The CATALOG .................................................................................38

Storing Data to Variables ................................................................ 39

Creating a Variable Name ..........................................................39

Storing a Value to a Variable Name ...........................................40

Storing an Unevaluated Expression............................................40

Storing an Answer......................................................................41

Copying a Variable Value ...........................................................41

Displaying a Variable Value........................................................ 41

Recalling a Variable Value..........................................................42

Classifying Variables as Data Types. ...............................................42

The CATLG-VARS (CATALOG-Variables) Menu...........................43

Selecting a Variable Name .........................................................44

The CUSTOM Menu.........................................................................44

Entering CUSTOM Menu Items................................................... 44

Clearing CUSTOM Menu Items...................................................45

Deleting a Variable from Memory ..............................................45

TI-86 Table of Contents

The CHAR (Character) Menu...........................................................45

The CHAR MISC (Miscellaneous) Menu...................................... 46

The CHAR GREEK Menu............................................................. 46

The CHAR INTL (International) Menu......................................... 46

Adding a Modifier to a Vowel ....................................................46

Chapter 3: Math, Calculus, and Test Operations 47

Keyboard Mathematical Functions .................................................48

The MATH Menu............................................................................. 49

The MATH NUM (Number) Menu............................................... 49

The MATH PROB (Probability) Menu.......................................... 50

The MATH ANGLE Menu............................................................ 51

The MATH HYP (Hyperbolic) Menu.............................................51

The MATH MISC (Miscellaneous) Menu..................................... 52

The InterpolateàExtrapolate Editor............................................ 53

The CALC (Calculus) Menu.............................................................. 54

The TEST (Relational) Menu............................................................55

Using Tests in Expressions and Instructions ............................... 56

Chapter 4: Constants, Conversions, Bases, and Complex Numbers 57

Using Built-In and User-Created Constants..................................... 58

The CONS (Constants) Menu...................................................... 58

The CONS BLTIN (Built-In Constants) Menu............................... 58

Creating or Redefining a User-Created Constant .......................60

The Constant Editor Menu..........................................................60

Entering a Constant Name in an Expression ..............................61

Converting Units of Measure ..........................................................61

Converting a Unit of Measure ....................................................61

The CONV (Conversions) Menu .................................................. 62

The CONV LNGTH (Length) Menu ..............................................63

The CONV AREA Menu...............................................................63

The CONV VOL (Volume) Menu..................................................63

The CONV TIME Menu................................................................63

The CONV TEMP (Temperature) Menu ....................................... 63

The CONV MASS Menu ..............................................................64

The CONV FORCE Menu.............................................................64

The CONV PRESS (Pressure) Menu ............................................. 64

The CONV ENRGY (Energy) Menu ..............................................64

The CONV POWER Menu............................................................64

The CONV SPEED Menu .............................................................64

Converting a Value Expressed as a Rate ....................................65

Number Bases .................................................................................65

Number Base Ranges .................................................................66

One’s and Two’s Complements .................................................. 66

The (Number) BASE Menu.......................................................... 66

The BASE Õ-Ú (Hexadecimal Characters) Menu.........................67

Entering Hexadecimal Digits.......................................................67

The BASE TYPE Menu.................................................................67

TI-86 Table of Contents

The BASE CONV (Conversion) Menu .......................................... 68

Converting Number Bases.......................................................... 68

The BASE BOOL (Boolean) Menu ...............................................68

Results of Boolean Operations ................................................... 69

The BASE BIT Menu.................................................................... 69

Using Complex Numbers................................................................. 70

Complex Results......................................................................... 70

Using a Complex Number in an Expression................................ 71

The CPLX (Complex Number) Menu........................................... 71

Chapter 5: Function Graphing 73

Defining a Graph............................................................................. 74

Setting the Graph Mode .................................................................74

The GRAPH Menu ........................................................................... 75

Using the Equation Editor ............................................................... 76

The Equation Editor (GRAPH y(x)=) Menu .................................76

Defining a Function in the Equation Editor ................................77

Notes about Defining Function Equations..................................78

Selecting Graph Styles................................................................ 79

Setting the Graph Style in the Equation Editor........................... 80

Using Shading Patterns to Differentiate Functions..................... 80

Viewing and Changing OnàOff Status of Stat Plots ................... 81

Setting the Window Variables......................................................... 81

Displaying the Window Editor.................................................... 82

Changing a Window Variable Value........................................... 82

Setting Graphing Accuracy with

Setting the Graph Format................................................................83

Displaying a Graph.......................................................................... 85

Pausing or Stopping a Graph in Progress ...................................85

Modifying a Drawn Graph..........................................................85

Graphing a Family of Curves ......................................................86

Smart Graph ............................................................................... 86

x and @y ...............................83

Chapter 6: Graph Tools 87

Graph Tools on the TI-86 ................................................................ 88

The GRAPH Menu.......................................................................88

Using the Free-Moving Cursor....................................................89

Graphing Accuracy .....................................................................89

Tracing a Graph...............................................................................90

Stopping and Resuming a Trace.................................................91

Resizing the Graph Screen with ZOOM Operations.........................91

The GRAPH ZOOM Menu ...........................................................91

Defining a Custom Zoom In........................................................ 93

Setting Zoom Factors..................................................................93

Zooming In and Zooming Out on a Graph..................................93

Storing and Recalling Zoom Window Variable Values................95

Using Interactive Math Functions ...................................................95

The GRAPH MATH Menu............................................................ 95

Settings That Affect GRAPH MATH Operations .......................... 96

Using ROOT, FMIN, FMAX, or INFLC ..........................................97

TI-86 Table of Contents

vii

Using ‰f(x), DIST, or ARC ............................................................98

Using dyàdx or TANLN............................................................... 99

Using ISECT .............................................................................. 100

Using YICPT.............................................................................. 100

Evaluating a Function for a Specified x......................................... 101

Drawing on a Graph......................................................................101

Before Drawing on a Graph .....................................................102

Saving and Recalling Drawn Pictures ....................................... 102

Clearing Drawn Pictures........................................................... 103

The GRAPH DRAW Menu ......................................................... 103

Shading Areas of a Graph ........................................................104

Drawing a Line Segment ..........................................................105

Drawing a Vertical or Horizontal Line ......................................106

Drawing a Circle.......................................................................106

Drawing a Function, Tangent Line, or Inverse Function ...........107

Drawing Freehand Points, Lines, and Curves ...........................107

Placing Text on a Graph........................................................... 108

Turning On or Turning Off Points .............................................108

Chapter 7: Tables 109

Displaying the Table......................................................................110

TABLE Menu............................................................................. 110

The Table.................................................................................. 110

Independent and Dependent Variables in the Table ................111

Navigating the Table................................................................ 111

The Table Menus ...................................................................... 112

Setting Up the Table .....................................................................113

Viewing and Editing Dependent Variable Equations ...............114

Clearing the Table.........................................................................114

Chapter 8: Polar Graphing 115

Preview: Polar Graphing ...............................................................116

Defining a Polar Graph..................................................................117

Setting Polar Graphing Mode...................................................117

The GRAPH Menu.....................................................................117

Displaying the Polar Equation Editor........................................118

Setting the Graph Screen Window Variables............................ 118

Setting the Graph Format.........................................................119

Displaying the Graph................................................................119

Using Graph Tools in Pol Graphing Mode.....................................119

The Free-Moving Cursor ........................................................... 119

Tracing a Polar Equation ..........................................................120

Moving the Trace Cursor to a q Value...................................... 121

Using Zoom Operations............................................................ 121

The GRAPH MATH Menu.......................................................... 122

Evaluating an Equation for a Specified q..................................122

Drawing on a Polar Graph........................................................122

viii

TI-86 Table of Contents

Chapter 9: Parametric Graphing 123

Preview: Parametric Graphing ......................................................124

Defining a Parametric Graph......................................................... 125

Setting Parametric Graphing Mode.......................................... 126

The GRAPH Menu.....................................................................126

Displaying the Parametric Equation Editor............................... 126

Selecting and Deselecting a Parametric Equation ....................127

Deleting a Parametric Equation................................................ 127

Setting the Graph Screen Window Variables............................ 127

Setting the Graph Format......................................................... 128

Displaying the Graph................................................................ 128

Using Graph Tools in Param Graphing Mode................................ 128

The Free-Moving Cursor........................................................... 128

Tracing a Parametric Function.................................................. 128

Moving the Trace Cursor to a t Value.......................................129

Using Zoom Operations............................................................ 129

The GRAPH MATH Menu.......................................................... 130

Evaluating an Equation for a Specified t ..................................130

Drawing on a Parametric Graph............................................... 130

Chapter 10: Differential Equation Graphing 131

Defining a Differential Equation Graph.........................................132

Setting Differential Equation Graphing Mode ..........................132

The GRAPH Menu.....................................................................133

Setting the Graph Format......................................................... 133

Displaying the Differential Equation Editor ..............................134

Setting the Graph Screen Window Variables............................ 135

Setting the Initial Conditions....................................................136

Setting the Axes .......................................................................137

Differential Equation Graphing Tips .........................................137

The Built-In Variable fldPic .......................................................138

Displaying the Graph................................................................138

Entering and Solving Differential Equations..................................139

Graphing in SlpFld Format........................................................ 139

Transforming an Equation into a First-Order System................ 140

Graphing in DirFld Format........................................................141

Graphing a System of Equations in FldOff Format....................142

Solving a Differential Equation for a Specified Value ...............144

Using Graph Tools in DifEq Graphing Mode .................................144

The Free-Moving Cursor ........................................................... 144

Tracing a Differential Equation................................................. 144

Moving the Trace Cursor to a t Value.......................................145

Drawing on a Differential Equation Graph ...............................145

Drawing an Equation and Storing Solutions to Lists.................145

Using ZOOM Operations...........................................................147

Drawing Solutions Interactively with EXPLR.............................148

Evaluating Differential Equations for a Specified t ...................150

TI-86 Table of Contents

Chapter 11: Lists 151

Lists on the TI-86 .......................................................................... 152

The LIST Menu.......................................................................... 152

The LIST NAMES Menu............................................................. 153

Creating, Storing, and Displaying Lists..........................................153

Entering a List Directly in an Expression................................... 153

Creating a List Name by Storing a List .....................................154

Displaying List Elements Stored to a List Name .......................154

Displaying or Using a Single List Element ................................155

Storing a New Value to a List Element..................................... 155

Complex List Elements .............................................................156

The List Editor ............................................................................... 156

The List Editor Menu ................................................................156

Creating a List Name in the Unnamed Column ........................ 157

Inserting a List Name into the List Editor .................................157

Displaying and Editing a List Element ......................................158

Deleting Elements from a List ..................................................158

Removing a List from the List Editor ........................................158

Using List Operations.................................................................... 159

The LIST OPS (Operations) Menu .............................................159

Using Mathematical Functions with Lists .....................................161

Attaching a Formula to a List Name .............................................162

Comparing an Attached List with a Regular List ......................163

Using the List Editor to Attach a Formula ................................163

Using the List Editor With Attached-Formula Lists ................... 164

Executing and Displaying Attached Formulas ..........................164

Handling Errors Related to Attached Formulas.........................165

Detaching a Formula from a List Name....................................166

Editing an Element of a Attached Formula List ........................166

Chapter 12: Vectors 167

Vectors on the TI-86 .....................................................................168

Creating, Storing, and Displaying Vectors.....................................169

The VECTR (Vector) Menu ........................................................169

The VECTR NAMES Menu.........................................................169

Creating a Vector in the Vector Editor......................................169

The Vector Editor Menu............................................................170

Creating a Vector on the Home Screen.....................................170

Creating a Complex Vector.......................................................171

Displaying a Vector...................................................................171

Using a Vector in an Expression ...............................................172

Editing Vector Dimension and Elements...................................172

The VECTR MATH Menu...........................................................173

The VECTR OPS (Operations) Menu..........................................173

The VECTR CPLX (Complex) Menu ...........................................175

Using Mathematical Functions with Vectors.................................176

Chapter 13: Matrices 177

Matrices on the TI-86....................................................................178

Creating, Storing, and Displaying Matrices ...................................178

TI-86 Table of Contents

The MATRX (Matrix) Menu ......................................................178

The MATRX NAMES Menu ....................................................... 178

Creating a Matrix in the Matrix Editor .....................................178

The Matrix Editor Menu ...........................................................179

Creating a Matrix on the Home Screen ....................................180

Creating a Complex Matrix ......................................................180

Displaying Matrix Elements, Rows, and Submatrices...............181

Using a Matrix in an Expression...............................................181

Editing Matrices in the Matrix Editor .......................................182

Editing Matrices on the Home Screen ......................................182

The MATRX MATH Menu .........................................................183

The MATRX OPS (Operations) Menu........................................ 184

The MATRX CPLX (Complex ) Menu......................................... 185

Using Mathematical Functions with Matrices............................... 185

Chapter 14: Statistics 187

Statistical Analysis on the TI-86.................................................... 188

Setting Up a Statistical Analysis.................................................... 188

The STAT (Statistics) Menu....................................................... 188

Entering Statistical Data........................................................... 189

The LIST NAMES Menu............................................................. 189

The STAT CALC (Calculations) Menu........................................ 189

Automatic Regression Equation Storage.................................. 191

Results of a Statistical Analysis..................................................... 192

The STAT VARS (Statistical Variables) Menu............................ 192

Plotting Statistical Data.................................................................194

The STAT PLOT Status Screen...................................................194

The STAT PLOT Menu ............................................................... 195

Setting Up a Stat Plot ............................................................... 195

Turning On and Turning Off a Stat Plot .................................... 195

The PLOT TYPE Menu (Selecting a Plot Type)...........................196

Plot Type Characteristics ..........................................................196

The STAT DRAW Menu..................................................................199

Forecasting a Statistical Data Value..............................................199

Chapter 15: Equation Solving 201

Preview: The Equation Solver........................................................202

Entering an Equation in the Equation-Entry Editor........................203

Setting Up the Interactive-Solver Editor........................................204

Entering Variable Values ..........................................................204

Controlling the Solution with Bounds and a Guess .................. 204

Editing the Equation.................................................................205

The Solver Menu.......................................................................206

Solving for the Unknown Variable ................................................206

Graphing the Solution...................................................................207

Solver Graph Tools........................................................................207

The Solver ZOOM Menu ...........................................................208

The Simultaneous Equation Solver................................................ 208

Entering Equations to Solve Simultaneously ............................208

Storing Equation Coefficients and Results to Variables............210

The Polynomial Root-Finder..........................................................211

TI-86 Table of Contents

Entering and Solving a Polynomial........................................... 211

Storing a Polynomial Coefficient or Root to a Variable ............ 212

Chapter 16: Programming 213

Writing a Program on the TI-86 ....................................................214

The PRGM Menu ...................................................................... 214

Creating a Program in the Program Editor ...............................214

The Program Editor Menu ........................................................ 215

The PRGM IàO (InputàOutput) Menu...................................... 215

The TI-86 Key Code Diagram ...................................................217

The PRGM CTL Menu ...............................................................218

Entering a Command Line........................................................ 220

Menus and Screens in the Program Editor ...............................220

Running a Program ....................................................................... 221

Breaking (Interrupting) a Program ...........................................222

Working with Programs ................................................................223

Managing Memory and Deleting a Program ............................ 223

Editing a Program.....................................................................223

Calling a Program from Another Program................................224

Copying a Program to Another Program Name........................ 225

Using and Deleting Variables within a Single Program ............225

Running an Assembly Language Program ....................................225

Entering and Storing a String........................................................ 226

The STRNG (String) Menu ........................................................227

Creating a String ......................................................................227

Chapter 17: Memory Management 229

Checking Available Memory .........................................................230

The MEM (Memory) Menu .......................................................230

Checking Memory Usage..........................................................230

Deleting Items from Memory ........................................................231

The MEM DELET (Delete) Menu ...............................................231

Resetting the TI-86 .......................................................................232

The MEM RESET (Reset) Menu.................................................232

ClrEnt (Clear Entry)...................................................................232

Chapter 18: The TI-86 Communication Link 233

TI-86 Linking Options....................................................................234

Linking Two TI-86s...................................................................234

Linking a TI-86 and a TI-85......................................................234

Linking a TI-86 and a CBL 2/CBL or CBR System......................234

Linking a TI-86 and a PC or Macintosh ....................................235

Downloading Programs from the Internet................................235

Connecting the TI-86 to Another Device.......................................235

The LINK Menu......................................................................... 236

Selecting Data to Send..................................................................236

The LINK SEND Menu...............................................................236

Initiating a Memory Backup .....................................................237

Selecting Variables to Send ......................................................238

The SEND WIND (Window Variables) Screen............................238

Sending Variables to a TI-85 ....................................................239

xii

TI-86 Table of Contents

The LINK SND85 (Send Data to TI-85) Menu ...........................239

Preparing the Receiving Device..................................................... 240

Transmitting Data .........................................................................240

Receiving Transmitted Data.......................................................... 241

Repeating Transmission to Several Devices .............................242

Error Conditions .......................................................................242

Insufficient Memory in Receiving Unit......................................242

Chapter 19: Applications 243

Using Math Operations with Matrices ..........................................244

Finding the Area between Curves................................................. 245

The Fundamental Theorem of Calculus......................................... 246

Electrical Circuits........................................................................... 248

Program: Taylor Series ..................................................................250

Characteristic Polynomial and Eigenvalues................................... 252

Convergence of the Power Series .................................................254

Reservoir Problem......................................................................... 256

Predator-Prey Model..................................................................... 258

Program: Sierpinski Triangle .........................................................260

Chapter 20: A to Z Function and Instruction Reference 261

Quick-Find Locator........................................................................ 262

Alphabetical Listing of Operations................................................ 266

Appendix 379

TI-86 Menu Map...........................................................................380

Handling a Difficulty......................................................................392

Error Conditions ............................................................................393

Equation Operating System (EOSé)..............................................397

Implied Multiplication ..............................................................397

Parentheses..............................................................................397

TOL (The Tolerance Editor)............................................................398

Computational Accuracy ............................................................... 399

Support and Service Information...................................................400

Product Support........................................................................400

Product Service.........................................................................401

Other TI Products and Services.................................................401

Warranty Information....................................................................402

Customers in the U.S. and Canada Only...................................402

Australia & New Zealand Customers Only................................403

All Customers outside the U.S. and Canada.............................404

Index

TI-86 Quick Start

Preparing to Use Your New TI-86........................................ 2

Calculating on the Home Screen.......................................... 3

Plotting Functions on the Graph Screen .............................. 9

M1 M2

F1 F2 F3

TI 86

Quick Start

After about four minutes of inactivity, the TI-86 turns off automatically.

If you release

or # while

adjusting the contrast, you

must press

again to

continue the adjustment.

Preparing to Use Your New TI-86

The brief examples in the TI-86 Quick Start demonstrate some common TI-86 features. Before you begin, you must install the batteries, turn on the calculator, adjust the contrast, and reset the memory and the defaults. Chapter 1 has more details on these topics.

Installing the AAA Batteries

Four AAA batteries are included in the TI-86 retail package. Remove the batteries from the package and install them in the battery compartment on the back of the calculator. Arrange

the batteries according to the polarity (+ and

Turning On and Turning Off the TI-86

To turn on the TI-86, press ^, which is in the bottom-left corner of the keyboard. You should see the entry cursor ( Å ) blinking in the top-left corner of the screen. If you do not see it, adjust the contrast (see below).

To turn off the calculator, press -, and then the key under

. This guidebook uses brackets ( ã and ä ) to express - and

keystroke combinations. For example, to turn off the TI-86, press - .

Adjusting the Contrast



Press and release the yellow - key.



Press and hold $ or # (above or below the half-shaded circle).

♦

To darken the screen contrast, press and hold $.

♦

To lighten the screen contrast, press and hold #.

) diagram in the battery compartment.

, which is

OFF

MODE

QUIT

EXIT

LINK

x-VAR

INS

DEL

alpha

ALPHA

2nd

RCL

BASE

CHAR

OFF

To express - and keystroke combinations, this guidebook places brackets

and

around the word

)

(

above the key to press.

The TI-86 on-screen division symbol is a forward slash

, as in a fraction.

( à )

Following evaluation, the entry cursor automatically moves to the next line, ready for a new entry.

When the TI-86 evaluates an expression, it automatically stores the answer to the builtin variable any previous value.

Ans

, replacing

Quick Start

Resetting All Memory and Defaults

To reset all memory and defaults, press -

Defaults set

are displayed on the home screen, confirming that all memory and defaults are

™ ( & )

. The messages

Mem cleared

and

reset. You may need to adjust the contrast after memory and default reset.

Calculating on the Home Screen

To replicate the screens shown in the Quick Start activities, reset all memory and defaults once before you begin. Before doing an activity, press before the entry retrieval and integer-part examples). Otherwise, the screens your TI-86 shows may differ from the screens pictured next to the activities.

Calculating the Sine of a Number



Enter the sine function. (



Enter a value. You can enter an expression, which is evaluated when you press



Evaluate the problem. The evaluation of the

expression sine(pà4) is displayed.

:) =

D - ~ F

Storing the Last Answer to a Variable



Paste the store symbol ( Since a value must precede not enter a value, the TI-86 automatically

Ans

pasted

before ¶. (

) to the screen.

, but you did

continued

(

)

to clear the screen (except

Quick Start

When ALPHA-lock is on and you press a key, the letters printed in blue above the keys are pasted to the screen. In the ex a m p l e , p r e s s

to enter a V.

You need not move the cursor to the end of the line to evaluate the expression.



Enter the variable name to which you want to store the last answer. ALPHA-lock is on.



Store the last answer to the variable. The stored value is displayed on the next line.

Using a Variable in an Expression



Enter the variable, and then square it. (:)



Evaluate. The value stored to the variable

is squared and displayed.

Editing an Expression



Enter the expression



Change



Move the cursor to the beginning of the

3.2

expression and insert a value. The insert cursor blinks between



Evaluate. The result is displayed. b

(25+14)(4N3.2)

2.3

. ! ! ! ! 2 "

and 25.

.(:)

\ 14 E

T 3 ` 2 E

- ! - p

3 3

negates a value, as in

subtracts, as in

An ellipsis (...) indicates that the result continues beyond the screen.

5N2=3

Displaying a Complex Number as a Result



Enter the natural log function. (:) B



Enter a negative number. D a



Evaluate. The result is displayed as a complex number.

Using a List with a Function



Enter the exponential function. (:) - ‚



Display the open brace (

On the TI-86, list.

menu, and then select the

LIST

{

) from the

{

specifies the beginning of a

LIST

menu.

b (press "

to display more)

- ”

LIST

Quick Start



Enter the list elements. Separate each element from the next with a comma.



Select the close brace (

}

) from the

menu to specify the end of the list.



Evaluate. The results of the constant raised to the 5th, 10th, and 15th powers are displayed as list elements.

LIST

P 10 P

b (press "

to display more)

Quick Start

Displaying the Integer Part of Real Numbers in a List



Display the automatically replaces the the last activity.)

Select

NUM



menu. The



Select the the

MATH NUM

menu. (The

MATH

to display the

menu shifts up.

MATH

iPart

(integer part) function from

iPart

menu.

MATH

menu from

LIST

MATH NUM

is pasted to the

- Œ

MATH

MATH NUM

screen. (The previous entry was left on the screen to illustrate the effect of

iPart

on the

previous answer.)

Paste

Ans

to the cursor location. (The



result list from the previous activity is stored to



Display the integer part of the result list

Ans

elements from the previous activity.

Removing (Exiting) a Menu



In the previous example, the

MATH NUM



Remove the

menu are displayed (- Œ &).

MATH NUM

menu from the screen. .

MATH

menu and the



Remove the

menu from the screen. .

MATH

Finding the Square Root



Paste the square root function to the screen. (:) - ˆ

Quick Start



Enter a value for which you want to find the square root.



Evaluate the expression. The square root of

144

is displayed.

Calculating Derivatives



Display the

der1



Enter an expression ( variable (



Evaluate. The first derivative of

respect to

menu, and then select

CALC

) with respect to a

) at a given point (8).

at 8 is displayed.

with

144

(:)

- †

(

CALC

2 I P 2 P 8 E

When you press TI-86 stores the expression or instruction you entered to the built-in memory storage area called

When expressing a measurement for a conversion, you do not enter a unit symbol manually. For example, you need not enter

Quick Start

ENTRY

to designate degrees.

, the

Retrieving, Editing, and Re-evaluating the Previous Entry



Retrieve the last entry from the previous

- ¢

example. (The last activity was not cleared.)



Edit the retrieved entry. ! !



Evaluate. The first derivative of respect to

at 3 is displayed.

with

Converting Degrees Fahrenheit to Degrees Celsius



Display the



Display the menu shifts up and



Enter the known measurement. If the measurement is negative, use parentheses. In this example, if you omit parentheses, the TI-86 converts 4¡F to about which it then negates (changes the sign of), returning a positive 15.5¡C.

Select

to designate Fahrenheit as the



known measurement unit. conversion symbol ( 4 ) are displayed after the measurement. (

menu. (:) - ’

CONV CONV TEMP

TEMP

menu. The

CONV

is highlighted.

D a

15.5¡C,

and the

continued

)

When storing to an equation variable using equation variable first, then and then the unevaluated expression. This is the opposite from the order for storing to most other variables on the TI-86.

, enter the

Quick Start





Select to which you want to convert.

Convert. The ¡C equivalent of displayed.

to designate Celsius as the unit

4¡F is

Storing an Unevaluated Expression to an Equation Variable



Enter the built-in equation variable



Enter the equals sign (=). 1



Enter an expression in terms of



Store the expression.

.(:) - n

The next section shows how to graph the functions

D = 2 E

y1=5(sin x)

and

y2=5(cos x)

Plotting Functions on the Graph Screen

The TI-86 plots four types of functions on the graph screen. To plot a graph, you must store an unevaluated expression to a built-in equation variable.

Each activity in this section builds upon the activity that precedes it. You must start here and perform the activities in the sequence in which they are presented. The first activity in this section assumes you are continuing from the last activity in the previous section.

Displaying and Entering Functions in the Equation Editor



Display the

GRAPH

menu. (

continued

) 6

Quick Start

In the equation editor, you must express each equation in terms of the independent variable mode only; Chapter 5).

To display up to seven graph styles, depending on the graphing mode, repeat

(in

Func

graphing

(





y(x)=

Select display the equation editor. unevaluated expression stored to

from the

GRAPH

menu to

5(sin x)

is the

previous activity. The equation editor menu is displayed as the lower menu.

Move the cursor down. The

y2=

prompt is

in the

equation editor menu

displayed.



Enter the expression

5(cos x)

at the

y2=

D > 2 E

prompt. Notice that the equals sign (=) of

is highlighted after you enter 5. Also,

the equals sign of

is highlighted. This indicates that both equations are selected to be graphed (Chapter 5).

Changing the Graph Style of a Function

In the equation editor, the icon to the left of each equation specifies the style in which the graph of that equation appears when you plot it on the graph screen.



Move the cursor to



Display the next menu group of the equation editor menu. ( 4 at the end of a menu group indicates that the menu has more items.)

Select

STYLE



menu to set ¼ (thick) graph style for

. $

from the equation editor

(

graph style icons

Plotting a Function on the Graph Screen





GRAPH

Select

from the

GRAPH

menu to plot the graph on the graph screen. The xand y-axes and

GRAPH

menu are displayed. Then each selected graph is plotted in the order in which it is listed in the equation editor.

When the graph is plotted, you can move the free-moving cursor (

) around the graph screen. The cursor coordinates are displayed at the bottom of the graph.

Tracing a Function





TRACE

Select

from the

GRAPH

menu to activate the trace cursor, with which you can trace along the graph of any selected function. The number of the current function (the

in y1) is displayed in the

top-right corner.

Move the trace cursor from the function to the function y2. The 1 in the top-right corner changes to the value of

; the y value changes to

x=0

. (

continued

)

- i

" # ! $

)

Quick Start

free-moving cursor

trace cursor

Quick Start

The window variables values determine the dimensions of the graph screen.



Trace the function displayed

5(cos x)

value is the solution for

at the current x value, which also

. As you trace, the

" and !

is displayed on the screen.

Evaluating y for a Specific x Value (During a Trace)



Enter a real number (or an expression that resolves to a real number) that is within the dimensions of the current graph screen. When you enter the first character,

the

prompt is displayed.



Evaluate

x=6

. The trace cursor moves directly to the solution. The or solution of the equation at

, is

displayed on the screen.

value,

Changing a Window Variable Value



Display the



Select

GRAPH

WIND

display the window editor.

(

menu. 6

from the

GRAPH

menu to

continued

)

Quick Start



Change the value stored in the window variable to 0.



Plot the graph on the redefined graph screen. Since fourth quadrants of the graph plane are displayed.

xMin=0

, only the first and

xMin

Deselecting a Function







y(x)=

Select display the equation editor and equation editor menu. The

y(x)=

and

Select menu to deselect the function equals sign is no longer highlighted.

Plot the graph on the graph screen. Since you deselected To select a function in the equation editor, repeat these steps. ( and deselects functions.)

from the

is highlighted.

SELCT

from the equation editor

GRAPH

, the TI-86 only plots y2.

SELCT

menu to

menu shifts up

y1=

both selects

. The

- i

Quick Start

Zooming In on a Portion of the Graph Screen



ZOOM

Select menu. The

ZOOM

is highlighted.

to display the

GRAPH

menu shifts up and

GRAPH ZOOM

(











BOX

Select to activate the zoom-box cursor.

Move the zoom-box cursor to a point that is to be a corner of the redefined graph screen, and then mark the point with a small square.

Move the cursor away from the small square to a point that is to be the opposite corner of the redefined graph screen. As you move the cursor, a rectangle is drawn on the graph.

Zoom in on the graph. The window variables change automatically to the specifications of the zoom box.

Clear the menus from the graph screen.

from the

GRAPH ZOOM

" # ! $ b

" # ! $

Operating

Installing or Replacing Batteries ........................................ 16

Turning On and Turning Off the TI-86 ...............................17

Adjusting the Display Contrast ..........................................17

The Home Screen............................................................... 18

Entering Numbers.............................................................. 19

Entering Other Characters .................................................20

Entering Expressions and Instructions ...............................24

Diagnosing an Error ........................................................... 27

Reusing Previous Entries and the Last Answer ..................28

Using TI-86 Menus ............................................................31

Viewing and Changing Modes........................................... 34

the TI-86

M1 M2

F1 F2 F3

TI 86

To express - and keystroke combinations, this guidebook places brackets

( ã and ä )

above the key to press. Do not remove the lithium

backup battery unless four fresh AAA batteries are in place. Properly dispose of the old batteries.

If you do not use your TI-86 frequently, the AAA batteries could last more than two weeks after the first lowbattery message.

Chapter 1: Operating the TI-86

around the word

Installing or Replacing Batteries

Your new TI-86 includes four AAA alkaline batteries. You must install them before you can turn on the calculator. A lithium backup battery is installed in the calculator already.



If the calculator is on, turn it off (press - ) to avoid loss of information stored in memory.



Slide the protective cover over the keyboard.



Holding the calculator upright, push down on the battery cover latch, and then remove the cover.



Remove all four old batteries.



Install four new AAA alkaline batteries, arranged according to the polarity (+ and N) diagram inside the battery compartment.



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.

When to Replace Batteries

When the AAA batteries are low, a low-battery message is displayed as you turn on the calculator. Generally, the calculator will continue to operate for one or two weeks after the low-battery message is first displayed. Eventually, the TI-86 will turn off automatically and will not operate until you replace the AAA batteries.

The lithium backup battery is inside the battery compartment, above the AAA batteries. It retains all memory when the AAA batteries are low or have been removed. To avoid loss of data, do not remove the lithium battery unless four fresh AAA batteries are installed. Replace the lithium backup battery about every three or four years.

Chapter 1: Operating the TI-86

Properly dispose of the old battery.

If you release

or # while

adjusting the contrast, you

must press

again to

continue the adjustment.

To replace the lithium backup battery, remove the battery cover and unscrew the tiny screw holding the

BACK UP BATTERY

according to the polarity (+ and

cover in place. Install a new

) diagram on the cover. Replace the cover and screw.

CR1616

CR1620

battery

Turning On and Turning Off the TI-86

To turn on the TI-86, press ^.

♦

previously had turned off the calculator by

If you pressing - , the TI-86 clears any errors and displays the home screen as it was last displayed.

♦

If Automatic Power Down

(APDTM) previously had turned off the calculator, the TI-86 will return as you left it, including the display, cursor, and any error.

To turn off the TI-86 manually, press - . All settings and memory contents are

retained by the Constant Memory

feature. Any error condition is cleared.

APD turns off the TI-86 automatically after about four minutes of non-use to extend battery life.

RCL

OFF

PRQ

CONV

CONS

BASE TES MEM

CHAR

STRNG

ANS

(

Adjusting the Display Contrast



Press and release the yellow - key.

MODE



Press and hold $ or # (above or below the half-shaded circle).

♦

To darken the screen contrast, press and hold $.

♦

To lighten the screen contrast, press and hold #.

2nd

alpha

ALPHA

QUIT

LINK

EXIT

x-VAR

INS

DEL

Chapter 1: Operating the TI-86

The TI-86 has 40 contrast settings, so each number

through 9 represents four

settings.

You need not clear the home screen to begin a new entry.

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

conditions. As you adjust, a number from

(lightest) to 9 (darkest) in the top-right corner indicates the current contrast setting. The number is not visible when the contrast is extremely light or dark.

As the batteries weaken over time, the actual contrast level of each number shifts. For

example, say you set the contrast to

need to set the contrast to

, then 5, then 6, and so on, to retain the original contrast level.

with fresh batteries. As the batteries weaken, you will

However, you need not replace the batteries until the low-battery message is displayed.

The Home Screen

When you first turn on your TI-86, the home screen is displayed. Initially, the home screen is a blank screen, except for the entry cursor ( Å ) in the top-left corner. If you do not see the cursor, press -, and then press and hold # or $ to adjust the contrast (page 17).

On the home screen, you can enter and evaluate expressions, and view the results. You also can execute instructions, store and recall variable values, and set up graphs and editors.

To return to the home screen from any other screen, press -

Displaying Entries and Answers

The home screen displays up to eight lines with a maximum of 21 characters per line. If an expression or series of instructions exceeds 21 characters and spaces, it automatically continues on the next line.

After all eight lines are full, text scrolls off the top of the display. You can press $ to scroll up the home screen, only as far as the first character in the current entry. To retrieve, edit, and re-execute previous entries, use -

(page 28).

Chapter 1: Operating the TI-86

e e

The mode settings control th way the TI-86 interprets expressions and displays answers (page 34).

The TI-86 on-screen division symbol is a forward slash

, as in a fraction.

( à )

Always use parentheses to clarify negation when you us conversion instructions (Chapter 4).

When an entry is executed on the home screen, the answer is displayed on the right side of the next line.

Done

When you execute an instruction,

is typically

Entry Answer

displayed on the right side of the next line.

If an answer is too long to display on the screen, an ellipsis (...) is displayed, initially to the right. To view

Entry Answer

more of the answer, press ". When you do, an ellipsis is displayed to the left. To scroll back, press !.

Entering Numbers

A symbol or abbreviation of each key’s primary function is printed in white on the key. For example, when you press \, a plus sign is pasted to the cursor location. This guidebook

1, 2, 3

describes number-entry keystrokes as

Entering Negative Numbers

To enter a negative number, press a (the negate key), and then press the appropriate

number keys. For example, to enter

number using T (the subtract key). a and T are two different keys with different uses.

The order in which the TI-86 evaluates negation and other functions within an expression is governed by the Equation Operating Systemè (Appendix). For example, the result of

, while the result of

to clarify the intended use of the negation symbol.

(L4)

is 16. If you are unsure about the order of evaluation, use D and

, and so on, instead of Y Z [.

, press a 5. Do not attempt to express a negative

In scientific notation only, one digit precedes the decimal.

In engineering notation, one, two, or three digits precede the decimal and the power of 10 exponent is a multiple of 3.

Chapter 1: Operating the TI-86

Using Scientific or Engineering Notation



Enter the mantissa (part of the number that precedes the exponent). This value can be an expression.





Paste

to the cursor location. C

If the exponent is negative, paste

to the cursor location.

Then enter a one-, two-, or three-digit exponent.



Evaluate the expression. b

D F 2 E

When you include scientific- or engineering-notation numbers in an expression, the TI-86 does not necessarily display answers in scientific or engineering notation. The mode settings (page 34) and the size of the number determine the notation of displayed answers.

Entering Complex Numbers

On the TI-86, the complex number a+bi is entered as in rectangular complex-number form or as



(

(a,b)

in polar

)

complex-number form. For more information about complex numbers, read Chapter 4.

Entering Other Characters

This is the 2nd key

This is the ALPHA key

2nd

alpha

ALPHA

QUIT

EXIT

LINK

x-VAR

MODE

INS

DEL

STAT

To enter a space within text,

1 ¤

press not valid within variable names.

For convenience, you can

press

commonly used

The

Name=

symbol automatically.

. Spaces are

instead of

to enter the

variable.

prompt and store

(¶)

set ALPHA-lock

Chapter 1: Operating the TI-86

The 2nd Key

The - key is yellow. When you press -, the cursor becomes Æ (the 2nd cursor). When you press the next key, the yellow character, abbreviation, or word printed above

- š

the

STAT

returns menu

that key is activated, instead of the key’s primary function.

The ALPHA Key

The

key is blue. When you press becomes ³ (the uppercase ALPHA cursor). When you press the next key, the blue uppercase character printed

, the cursor

STAT

returns an

above that key is pasted to the cursor location.

When you press lowercase alpha cursor). When you press the next key, the

, the cursor becomes Ï (the

STAT

- n

returns an

lowercase version of the blue character is pasted to the cursor location.

ALPHA-lock and alpha-lock

To enter more than one uppercase or lowercase alpha character consecutively, set ALPHAlock (for uppercase letters) or alpha-lock (for lowercase letters).

To set ALPHA-lock when the entry cursor is displayed, press

♦

To cancel ALPHA-lock, press

♦

To switch from ALPHA-lock to alpha-lock, press -

1 1

To set alpha-lock when the entry cursor is displayed, press -

♦

To cancel alpha-lock, press

1 1

n 1

Chapter 1: Operating the TI-86

In most cases, the appearance of the cursor indicates what will happen when you press the next key.

Graphs and editors sometimes use additional cursors, which are described in other chapters.

♦

To switch from alpha-lock to ALPHA-lock, press

You can use - when ALPHA-lock or alpha-lock is on. Also, if you press a key that has no blue character above it, such as

6, 3

, or !, the key’s primary function still applies.

Common Cursors

Entry

Insert

Second

LPHA

alpha

Full

♦ ♦ ♦

Enters a character at the cursor, overwriting any existing character

Inserts a character at the cursor location and shifts remaining characters right

Enters a 2nd character or executes a 2nd operation (yellow on the keyboard)

Enters an uppercase ALPHA character (blue on the keyboard)

Enters the lowercase version of an ALPHA character (blue on the keyboard)

Accepts no data; maximum characters are entered at a prompt or memory is full

If you press

If you press -

after - p, the cursor becomes an underlined

(A).

If you press - after - p, the insert cursor becomes an underlined # (

(a).

The entry cursor overwrites characters.

( Å )

Chapter 1: Operating the TI-86

Cursor Direction Keys

$ scrolls/moves cursor up

$ darkens screen contrast

moves cursor left

! moves cursor to beginning of entry

# scrolls/

- #

moves cursor down

lightens screen contrast

- "

If you hold down ", #, !, or $, the cursor continues to move.

Inserting, Deleting, and Clearing Characters

- p

3 :

Changes the cursor to the insert cursor ( __ ); inserts characters at the insert cursor and shifts remaining characters right; to cancel insert, press - p or press ", #, !, or

Deletes a character at the cursor; to continue deleting to the right, hold down

Clears the current entry on the home screen;

: :

moves cursor right

moves cursor to end of entry

clears the entire home screen

Chapter 1: Operating the TI-86

Entering Expressions and Instructions

Entering an Expression

An expression is any combination of numbers and variables that serve as arguments for one or more functions. On the TI-86, you typically enter an expression in the same order as you would write it on paper. For example,

You can use an expression on the home screen to calculate an answer.

In most places where a value is required, you can use an expression to enter the value.

For example, enter an expression as a window variable value (Chapter 5). When you press #, $, evaluates the expression and replaces it with the result.

To enter an expression, you enter numbers, variables, and functions from the keyboard and menus (page 31). When you press location) according to EOS order-of-evaluation rules (Appendix), and the answer is displayed.

To enter the expression 3.76 ÷ ( then evaluate it, you would press these keys:

` 76 F D a 7 ` 9 \ - ˆ 5 E \ 2 < 45

5 tan xStat

7.9 + ‡5) + 2 log 45 and

, or

, the expression is evaluated (regardless of the cursor

, and

, the TI-86

40((L5+3)N(2+3))

are expressions.

In this guidebook, optional arguments are shown in brackets include these brackets when you enter the arguments.

The A to Z Reference describes all TI-86 functions and instructions, including their required and optional arguments.

In the the first item beginning with a letter, press that letter (as in

ãLä

and ä ). Do not

(

CATALOG

in the example).

, to move to

Chapter 1: Operating the TI-86

Using Functions in Expressions

A function returns a value. Some examples of functions are

, + , ‡ , and

log

. To use

functions, you usually must enter one or more valid arguments.

When this guidebook describes the syntax of a function or instruction, each argument is in

angle

sin

italics. For example:

. Press = to enter

measurement (or an expression that resolves to

sin

, and then enter a valid

angle

). For functions or instructions with

angle

more than one argument, you must separate each argument from the other with a comma.

Some functions require the arguments to be in parentheses. When you are unsure of the evaluation order, use parentheses to clarify a function’s place within an expression.

Using an Instruction

ClDrw

An instruction initiates an action. For example,

is an instruction that, when executed, clears all drawn elements from a graph. You cannot use an instruction in an expression. Generally, the first letter of each instruction name is uppercase on the TI-86. Some

(

instructions take more than one argument, as indicated by an open parenthesis ( end of the name. For example,

Circl(

requires three arguments,

Circl(x,y,

radius

) at the

)

Entering Functions, Instructions, and Operators

log 45

You can enter a function, instruction, or operator in any of three ways (

♦

Paste it to the cursor location from the keyboard or a menu (<

♦

Paste it to the cursor location from the

♦

Enter it letter by letter ( -

CATALOG

n 1

ãLä ãOä ãGä

w &

1 1

, for example).

& &

45).

As you can see in the example, using the built-in function or instruction typically is easier.

Chapter 1: Operating the TI-86

When you select a function, instruction, or operator, a symbol comprising one or more characters is pasted to the cursor location. Once the symbol is pasted to the cursor location, you can edit individual characters.

In the example, the indicates that the value before it is to be stored to the variable after it (Chapter 2). To paste press

to the screen,

symbol

For example, assume that you pressed -

yMin

to the cursor location as part of an expression. Then you realized you wanted

Instead of pressing nine keys to select

w / / * & & b

xMin

, you can simply press ! ! ! !

to paste

xMin

Entering Consecutive Entries

To enter two or more expressions or instructions consecutively, separate each from the next with a colon (- ). When you press

, the TI-86 executes each entry from left to right and displays the result of the last expression or instruction. The entire group entry is stored in last entry (page 28).

The Busy Indicator

When the TI-86 is calculating or graphing, a moving vertical line is displayed as the busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator is replaced by the pause indicator, a moving vertical dotted line.

Interrupting a Calculation or Graph

To interrupt a calculation or graph in progress, press ^. When you interrupt a calculation,

ERROR 06 BREAK

the

♦

To return to the home screen, select

♦

To go to the beginning of the expression, select

message and menu are displayed.

QUIT

(press *).

GOTO

(press &). Press

recalculate the expression.

Chapter 1: Operating the TI-86

Chapter 5: Function Graphin introduces graphing.

If a syntax error occurs within a stored equation during program execution, select

GOTO

to return to the equation editor, not to the program (Chapter 5).

When you interrupt a graph, a partial graph and the

♦

To return to the home screen, press

♦

To restart graphing, select an instruction that displays the graph.

: :

GRAPH

menu are displayed.

or any non-graphing key.

Diagnosing an Error

When the TI-86 detects an error, it returns an error message, such as

ERROR 04 DOMAIN

The Appendix describes each error type and possible reasons for the error.

♦

If you select

♦

If you select

QUIT

(or press -

), the home screen is displayed.

GOTO

, the previous screen is displayed with the cursor on or near the error.

Correcting an Error



Note the error type (







GOTO

Select

Determine the cause for the error. If you cannot, refer to the Appendix for possible causes.

Correct the error and continue.

, if available. The previous screen is displayed with the cursor on or near the error.

ERROR ## errorType

ERROR 07 SYNTAX

Chapter 1: Operating the TI-86

Reusing Previous Entries and the Last Answer

Retrieving the Last Entry

When you press instruction, the entire expression or instruction is placed in a storage area called (last entry). When you turn off the TI-86,

on the home screen to evaluate an expression or to execute an

is retained in memory.

ENTRY

To retrieve the last entry, press -

. The current

line is cleared and the entry is pasted to the line.

Retrieving and Editing the Last Entry



On the home screen, retrieve the previous entry.



Edit the retrieved entry.



Re-execute the edited entry.

- ¢

! ! ! ! !

Retrieving Previous Entries

The TI-86 retains as many previous entries as possible in

, up to a capacity of 128

ENTRY

bytes. To scroll from the newest to the older previous entries stored to

- ¢

. If you press -

stored entry is displayed again; continuing to press -

after displaying the oldest stored entry, the newest

repeats the order.

ENTRY

, repeat

Consecutively entered entries

)

separated by colons (page 26 are stored as one entry.

The formula for finding the area of a circle is

The equation solver (Chapter

15) is another tool with which you can perform this task.

A=pr

Chapter 1: Operating the TI-86

Retrieving Multiple Entries

To store two or more expressions or instructions together to line, separating each from the other with a colon, and then press the entire group is stored in

. The example below shows one of many ways you can

ENTRY

, enter them on one

ENTRY

. Upon execution,

manipulate this feature to avoid tedious manual re-entry.



Use trial and error to find the radius of a circle with an area of 200 square centimeters. Store guess, then execute



Retrieve new guess. Continue guessing to approach the answer of

8¶r:pr

to r as your first

and insert

200

7.958

as a

X - n

] - ~

[

1 I b

- ¢

- ! b

- p `

958

Clearing the ENTRY Storage Area

To clear all data from the

ClrEnt

select

from the

MEM

storage area, begin on a blank line on the home screen,

ENTRY

menu (press -

™ *

), and then press

Retrieving the Last Answer

When an expression is evaluated successfully on the home screen or in a program, the TI-86

Ans

stores the answer to a built-in variable called

(last answer).

complex number, list, vector, matrix, or string. When you turn off the TI-86, the value in

Ans

may be a real or

Ans

is retained in memory.

Chapter 1: Operating the TI-86

147

tomatoes.

Ans

to the cursor location, press - ¡. You can use the

Ans

1.7

meters

` 7

147

F -

To copy the variable name

Ans

variable

anywhere that the value stored to it is valid. When the expression is evaluated,

the TI-86 calculates the result using the value stored in



Calculate the area of a garden plot

4.2

meters.



Calculate the yield per square meter if the plot produces a total of

Using Ans Preceding a Function

Previous answers are stored to

Ans

. If you begin an expression by entering a function that

requires a preceding argument, the TI-86 automatically enters



Enter and execute an expression.



Enter a function without an argument. pasted to the screen, followed by the function.

Ans

Storing Results to a Variable



Calculate the area of a circle with radius meters.



Calculate the volume of a cylinder of radius meters and height



Store the result to the variable V.

3.3

meters.

- ~ b

X b

Ans

as the argument.

Chapter 1: Operating the TI-86

Using TI-86 Menus

The symbols for many TI-86 features are found in menus instead of on the TI-86 keyboard.

Displaying a Menu

The way to display a particular menu depends on the menu’s location on the TI-86.

Menu-Displaying Method Example

Press a key that has a menu name on it

Press - and then a 2nd-key menu name -

Select a menu name from another menu -

Select an editor or selection screen - ” ) displays the list editor menu with the list editor

ccidentally commit an error 1

displays the

Œ Œ &

X b

displays the

GRAPH

MATH

displays the

displays the error menu

MATH NUM

Some TI-86 menus have as many as 25 items.

", #, !

work on menus.

, and $ do not

When you display a menu, a menu group of one to five items is displayed on the bottom of the screen. If the more symbol ( 4 ) is displayed after the fifth item in a menu group, the menu continues for at least one more menu group. To view the next menu group, press

. The

last menu group of one to five items does not have a 4 symbol.

For example, press -

When you see 4 here...

to display

the

...press / to display the next menu group.

MATH

menu.

From the last menu group, press again to return to the first menu group.

The Appendix Menu Map shows every TI-86 menu.

Typically, a TI-86 menu item is five characters long or less.

menu; it does not scroll the upper menu.

Chapter 1: Operating the TI-86

only scrolls the lower

The Menu Keys

upper menu keys

lower menu keys

- l

- e

upper menu items

clears all menus

through i selects

M1 M2 M3 M4 M5

' ( )

QUIT

- . /

/ scrolls lower menu groups

removes the lower menu

Selecting a Menu Item

When you display a menu, one to five items are displayed. To select a menu item, press the menu selection key directly below the item. For example, in the

NUM

press & to select

, press ' to select

menu to the right,

MATH

PROB

, and so on.

& ' ( )

When you select a menu item that displays another menu, the first menu moves up one line on the screen to make room for the new menu. All items on the original menu are displayed in reverse type, except the item you selected.

When you select

NUM

...

...the

MATH

menu moves up and the

MATH NUM

menu is displayed.

To remove the move the

MATH

MATH NUM

menu down, press ..

menu and

Chapter 1: Operating the TI-86

To select an item from the upper menu, press - and the appropriate key e through i.

To remove a menu from the bottom of a graph screen,

press graph (Chapter 5).

after plotting th

To select To select

PROB

from the upper menu, press

iPart

from the lower menu, press

- f

When an editor menu is displayed as the upper menu, and you select an item from the lower menu that displays yet another menu, the editor menu remains as the upper menu.

When you select

Upper: equation editor menu Lower:

MATH

NUM

from the lower menu... The

...the equation editor menu remains and the

MATH NUM

menu is displayed.

Upper: equation editor menu Lower:

menu disappears.

MATH

MATH NUM

Exiting (Removing) a Menu

To remove the lower menu from the screen, press

...the

When you press ....

Upper: Lower:

MATH MATH NUM

menu Lower:

MATH NUM

and the

menu moves down.

MATH

menu No menu

MATH

menu disappears

Press the

MATH

again, and

menu disappears.

In the screen to the right, the default mode settings are highlighted along the left side of the screen.

This example changes the decimal mode setting to 2, as in U.S. dollars and cents.

In answer is more than 12 digits or the absolute value of the answer < .001, it is displayed in scientific notation.

Notation modes do not affect how you enter numbers.

Chapter 1: Operating the TI-86

Normal

notation, if the

Viewing and Changing Modes

To display the mode settings, press settings are highlighted. Mode settings control how the TI-86 displays and interprets numbers and graphs. The Constant Memory feature retains current mode settings when the TI-86 is turned off. All numbers, including elements of matrices and lists, are displayed according to the mode settings.

Changing a Mode Setting



Move the cursor to the line of the setting that you want to change (decimal setting in the example).



Move the cursor to the setting you want (2 decimal places).



Execute the change.

Notation Modes

Normal Sci

Eng

Displays results with digits to the left and right of the decimal (as in

(scientific) Displays results in two parts: significant digits (with one digit to the left of the decimal) are displayed to the left of to the right of

(engineering) Displays results in two parts: significant digits (with one, two, or three digits to the left of the decimal) are displayed to the left of of 10 (which is always a multiple of 3) is displayed to the right of

(as in

1.234567E5

. The current

" " "

and the appropriate power of 10 is displayed

)

123456.7

and the appropriate power

(as in

)

123.4567E3

)

Non-decimal modes are valid

only on the home screen or i the program editor.

Decimal Modes

Float

(fixed) (

(floating) Displays results up to 12 digits, plus any sign and the floating decimal point

012345678901

digits to the right of the decimal point (rounds answers to the specified decimal place); the second

Angle Modes

Radian Degree

Interprets angle values as radians; displays answers in radians

Interprets angle values as degrees; displays answers in degrees

Complex Number Modes

RectC PolarC

(rectangular complex mode) Displays complex-number results as

(polar complex mode) Displays complex-number results as

Graphing Modes

Func Pol Param DifEq

(function graphing) Plots functions where y is a function of

(polar graphing) Plots functions where r is a function of

(parametric graphing) Plots relations where x and y are functions of

(differential equation graphing) Plots differential equations in terms of

Number Base Modes

Dec Bin Oct Hex

(decimal number base) Interprets and displays numbers as decimal (base 10)

(binary number base) Interprets numbers as binary (base 2); displays Ü suffix with answers

(octal number base) Interprets numbers as octal (base 8); displays Ý suffix with answers

(hexadecimal number base) Interprets numbers as hexadecimal (base 16); displays suffix with answers

Chapter 1: Operating the TI-86

; each number is a setting) Displays results with the specified number of

sets 10; the second 1 sets 11

(real,imaginary)

(magnitude

angle)

Chapter 1: Operating the TI-86

Vector modes do not affect how you enter vectors.

The value stored to

dxNDer

(Appendix).

affects

Vector Coordinate Modes

RectV

CylV

SphereV

(rectangular vector coordinates) Displays answers in the form vectors and

(cylindrical vector coordinates) Displays results in the form vectors and

(spherical vector coordinates) Displays results in the form ãr ± vectors and

Differentiation Modes

dxDer1

dxNDer

(exact differentiation) Uses value for each function in an expression ( restricts the kinds of functions that are valid in the expression)

(numeric differentiation) Uses for an expression ( are valid in the expression)

x y z

for three-element vectors

der1

dxNDer

is less accurate than

x y

for two-element

(Chapter 3) to differentiate exactly and calculate the

dxDer1

is more accurate than

nDer

to differentiate numerically and calculate the value

dxDer1

, but more kinds of functions

dxNDer

, but it

The CATALOG,

The CATALOG .................................................................... 38

Storing Data to Variables................................................... 39

Classifying Variables as Data Types................................... 42

The CUSTOM Menu ...........................................................44

The CHAR (Character) Menu.............................................. 45

Variables, and Characters

M1 M2

F1 F2 F3

TI 86

Chapter 2: The

CATALOG

, Variables, and Characters

The

CATALOG

item on the menu.

is the first

CATLG-VARS

The CATALOG

The

CATALOG

do not begin with a letter (such as

displays all TI-86 functions and instructions in alphabetical order. Items that

- w &

Bin

) are at the end of the

CATALOG

The selection cursor ( 4 ) indicates the current item. To select an item from the move the selection cursor to the item and press b. The

CATALOG

disappears and the

name is pasted to the previous cursor location.

Use # or to move 4 to an item...

...and press The item is pasted to the cursor location.

To jump... Do this:

To the first item beginning with a particular letter Press the letter; ALPHA-lock is on

BLANK

CATALOG

are on the

Press $ from the first

PAGE PAGE

CATALOG

CUSTOM

menu of up to 15

To special characters at the end of the Down one whole screen Select Up one whole screen Select

The menu items

CUSTM

and With them, you can create and edit your own variables, including program names. For details about the

from the

menu and each

CUSTOM

CATALOG

CATALOG CATALOG

VARS

CATALOG

menu, read page 44.

CATALOG

item

menu ( & ) menu ( ' )

screen menu.

items and

This chapter describes the first two data storage methods listed here. The other methods are described in the appropriate chapters.

Chapter 2: The

CATALOG

, Variables, and Characters

Storing Data to Variables

On the TI-86, data can be stored to variables in several ways. You can:

♦ ♦ ♦ ♦ ♦

The TI-86 has built-in variable names with specific purposes, such as equation variables, list names, statistical result variables, window variables, and of them. They are introduced in the appropriate chapters of this guidebook.

Creating a Variable Name

You can create your own variable name when you use data. When you create a user-created variable name, follow these guidelines.

♦ ♦

♦

Use Use Use an editor’s

to store a value to a variable.

to store an unevaluated expression to an equation variable.

Name=

prompt to store several types of data to a variable. Change TI-86 settings or reset defaults and memory to the factory settings. Execute functions that cause the TI-86 to store data automatically to built-in variables.

Ans

. You can store values to some

Name=

, or a

prompt to store

The user-created variable name can be from one to eight characters long. The first character must be a letter, which includes all

as Ñ, ñ, Ç, and ç from the

CHAR MISC

menu.

CHAR GREEK

menu items, as well

A user-created variable name cannot replicate a TI-86 feature symbol or built-in variable. For example, you cannot create function symbol. You cannot create

Ans

abs

, because

, because it is already a built-in variable name.

abs

is the absolute value

The TI-86 distinguishes between uppercase and lowercase characters in variable names. For example,

Ans

only

is a built-in variable name;

ANS, Ans

, and

ans

are three different variable names. Therefore,

ANS

and

ans

can be user-created variable names.

Chapter 2: The

CATALOG

, Variables, and Characters

Storing a Value to a Variable Name



Enter a value, which can be an expression. - ~



Enter ¶ (the store symbol) next to the value. X



Create a variable name one to eight characters long, starting with a letter. ALPHA-lock is on.



Store the value to the variable. The value stored to the variable is displayed as a result.

Storing an Unevaluated Expression

When you store an expression to memory using evaluated and the result is stored to a variable.

ä ãRä ãEä ãAä

(with the ¶ sign), the expression is

When you use =, first, then In contrast, when you use

is first, then ¶, then

value

variable

, then

variable expression

When you store an unevaluated expression using

, or the equation editor

(Chapter 5), or the equation solver (Chapter 15), the unevaluated expression is stored to an equation variable.

To store an unevaluated expression on the home screen or in a program, the syntax is:

variable

where You can use

expression

variable

always precedes the equals sign and

to store a mathematical expression to an equation variable. For example,

expression

always follows the equals sign.

F=M¹A

In the example, the TI-86 multiplies the value stored to

AREA

To paste location, you can press

w (

selection cursor and press

To paste location, press

times

AREA

to the cursor

3.3

to the cursor

, move the

(4)

AREA

Chapter 2: The

CATALOG

, Variables, and Characters

Storing an Answer

To store an answer to a variable before you evaluate another expression, use



Enter and evaluate an expression.



Store the answer to a user-created variable or to a valid built-in variable.

The value stored to the variable is displayed as a result.

1 1

ä ãRä ãEä ãAä

` 3

ä ãOä ãLä

Copying a Variable Value

To copy the contents of

variableA

into

variableB

, the syntax is:

variableA¶variableB

and

Ans

To paste a variable name, you can select it from a menu (page 42).

VARS

For example,

RegEq¶y1

stores the regression equation (Chapter 14) to the variable y1.

Displaying a Variable Value



With the cursor on a blank line on the home screen, paste the variable name to the cursor location, as described above.



Display the contents of the variable.

- w ( #

(location may

vary)

You also can display variables containing some data types by displaying them in the appropriate editor (such as the list editor or window variable editor) or graph. These methods are detailed in subsequent chapters of this guidebook.

To cancel

Editing a recalled value does not change the value stored to the variable.

When you store data in an editor, the TI-86 recognizes the data type according to th editor. For example, only vectors are stored using the vector editor.

Chapter 2: The

, press

RCL

CATALOG

, Variables, and Characters

Recalling a Variable Value



Move the cursor to where you want to insert the recalled variable value.



Display the

Rcl

prompt at the bottom of

the screen. ALPHA-lock is on.



Enter the variable name you want to recall.



Recall the variable contents to the cursor location. The

Rcl

prompt disappears and

the entry cursor returns.

100

- –

[V] [O] [L]

Classifying Variables as Data Types

The TI-86 classifies variables according to data type and places each variable on a data-type selection screen. You can display each screen by selecting the appropriate data type from the

CATLG-VARS

If data... The TI-86 classifies the data type as... For example:

Begins with { and ends with Begins with ã and ends with Begins with ãã and ends with ää A matrix (

menu, as described on page 43. Here are some examples.

}

A list (

VARS LIST

A vector (

VARS VECTR

screen)

VARS MATRX

screen)

{1,2,3}

1,2,3

ãã

1,2,3äã4,5,6äã7,8,9

ää

Chapter 2: The

CATALOG

, Variables, and Characters

To display additional menu groups, press

The list names

yStat

and variables on the screen.

fStat, xStat

are statistical resul

VARS STAT

The CATLG-VARS (CATALOG-Variables) Menu

CATLG ALL REAL CPLX LIST

CATLG ALL REAL CPLX

LIST VECTR MATRX STRNG EQU CONS PRGM GDB PIC STAT WIND

Displays the Displays a selection screen with all variables and names of all data types Displays a selection screen with all real number variables Displays a selection screen with all complex number variables Displays a selection screen with all list names Displays a selection screen with all vector names Displays a selection screen with all matrix names Displays a selection screen with all string variables Displays a selection screen with all equation variables Displays a selection screen with all user-defined constants Displays a selection screen with all program names Displays a selection screen with all graph database names Displays a selection screen with all picture names Displays a selection screen with all statistical result variables Displays a selection screen with all window variables

CATALOG

- w

VECTR MATRX STRNG EQU CONS

PRGM GDB PIC STAT WIND

The example assumes that the real-number variables

AREA

example on page 41 have no been deleted from memory.

Chapter 2: The

VOL

and

from the

CATALOG

, Variables, and Characters

Selecting a Variable Name



Select the appropriate data-type selection screen from the



Move the cursor to the variable you want to select.



Select the variable you want. b

CATLG-VARS

menu.

- w (

When copying items into the

CUSTOM

menu cells and menu groups.

menu, you can skip

The CUSTOM Menu

You can select up to 15 items from the

- w & (

CATALOG

and instructions, and other items -- to create your own menu, press

. Use & through * and

Entering CUSTOM Menu Items











CUSTM

Select

CUSTOM

Move the selection cursor ( 4 ) to the item you want to copy to the

Copy the item to the select, replacing any previous item.

To enter more items, repeat steps 2 and 3 using different items and cells.

Display the

from the

menu is displayed. ALPHA-lock is on.

CUSTOM

CATALOG

CUSTOM

menu. -l 9

. The

menu.

menu cell you

screens -- program names, functions,

VARS

CUSTOM

menu. To display your

CUSTOM

to select items like any other menu.

- w & (

# # #

(

To clear an item from the second or third menu group,

press displayed, and then select it.

You cannot delete a TI-86 built-in variable.

You cannot delete a program variable using

until the item is

DelVar(

Chapter 2: The

CATALOG

, Variables, and Characters

Clearing CUSTOM Menu Items







BLANK

Select

CUSTOM BLANK

Clear the menu item. To clear more items, repeat steps 2 and 3.

from the

CATALOG

menu is displayed.

menu. The

- w & )

(

Deleting a Variable from Memory

From the home screen or in a program, to delete from memory one user-created variable name (except a program name) and its contents, the syntax is:

DelVar(

variable

)

To delete user-created variable names and their contents (including program names), display the

MEM DELET

(Chapter 16). Deleting a variable does not remove it from the

menu (-

™ '

), select the data type, select the variable, and then press

CUSTOM

menu (page 44).

The CHAR (Character) Menu

MISC GREEK INTL

miscellaneous international characters characters menu menu Greek characters menu

- Ÿ

Chapter 2: The

CATALOG

, Variables, and Characters

Ñ, ñ, Ç

, and ç are valid as any character of a variable name, including the first letter.

%, '

, and ! can be functions.

All

CHAR GREEK

are valid variable-name characters, including the first

letter.

( - ~ )

as a character; constant on the TI-86.

menu items

is not valid

is a

The CHAR MISC (Miscellaneous) Menu -

Ÿ &

MISC GREEK INTL

?#&%'

The CHAR GREEK Menu -

Ÿ '

!@$~ |

¿ÑñÇç

MISC GREEK INTL

abg@d4H qlmr

The CHAR INTL (International) Menu -

4G s

Ÿ (

MISC GREEK INTL

´`^¨

You can combine modifiers on the

CHAR INTL

menu with uppercase or lowercase vowels to

create vowels used in some languages. You can use these vowels in variable names and text.

Adding a Modifier to a Vowel



Select the modifier from the

CHAR INTL

menu. ALPHA-lock is on. If necessary, switch to alpha-lock.



Enter the uppercase or lowercase vowel over which you want the modifier.

- Ÿ ( )

- n

Math, Calculus,

Keyboard Mathematical Functions ....................................48

The MATH Menu................................................................ 49

The CALC (Calculus) Menu ................................................54

The TEST (Relational) Menu............................................... 55

and Test Operations

M1 M2

F1 F2 F3

TI 86

)

The A to Z Reference details which data types are valid arguments for each function.

The most common mathematical functions are on the TI-86 keyboard. For syntax, details, and example of these functions, refer to the A to Z Reference.

is equivalent to the reciprocal, 1àx.

Chapter 3: Math, Calculus, and Test Operations

(the multiplicative inverse

Keyboard Mathematical Functions

You can use these mathematical functions in expressions with real or complex values. You can use some of them with lists, vectors, matrices, or strings.

When you use lists, vectors, or matrices, the valid functions return a list of results calculated on an element-by-element basis. If you use two lists, vectors, or matrices in the same expression, they must be equal in dimension.

Key Function Key Function

\ T M F a I

- ˆ

- ƒ @

- z C

(add)

(subtract)

(multiply)

(divide)

(negate)

(square)

‡

(square root)

(inverse)

(raise to a specified power)

10^

(10 to a specified power)

(exponent)

= > ?

- {

- |

- } < B

- ‚

- ~

sin

(sine)

cos

(cosine)

tan

(tangent)

sin

(arcsine; inverse of sine)

cos

(arccosine; inverse of cosine)

tan

(arctangent; inverse of tangent)

log

(logarithm)

(natural log)

(constant e raised to a power)

(constant pi; 3.1415926535898)

Chapter 3: Math, Calculus, and Test Operations

value

can sometimes be an expression, list, vector, or matrix. For details about specific syntax options and examples, refer to the A to Z Reference.

The MATH Menu

NUM PROB ANGLE HYP MISC

number angle miscellaneous math menu menu functions menu

probability hyperbolic interpolate menu menu editor

The MATH NUM (Number) Menu -

- Œ

Œ &

NUM PROB ANGLE HYP MISC

round iPart fPart int abs

value

round(

value

iPart

value

fPart

value

int

value

abs

value

sign

valueA,valueB

min(

list

min( max( max( mod(

)

valueA,valueB list

)

numberA,numberB

#ofDecimals

[

)

]

Rounds

)

Returns the integer part or parts of Returns the fractional part or parts of Returns the largest integer less than or equal to Returns the absolute value or magnitude of Returns Returns the smaller of Returns the smallest element of Returns the larger of Returns the largest element of Returns

)

value

numberA

to 12 decimal places or to

value

is positive; 0 if

modulo

INTER

sign min max mod

#ofDecimals

value

is 0;

value

valueA

and

value

valueB

list

valueA

and

valueB

list

numberB

is negative

Chapter 3: Math, Calculus, and Test Operations

(factorial) is valid for non-

integers.

randInt, randNorm randBin

are abbreviated in

the

MATH PROB

, and

menu.

The MATH PROB (Probability) Menu -

NUM PROB ANGLE HYP MISC

! nPr nCr rand randIn

value

items

rand

randInt(

randNorm(

stdDeviation

randBin(

number

nPr

number

nCr

lower,upper

#ofTrialsä

#ofTrials

)

mean

)

probabilityOfSuccess

#ofSimulationsä

)

Returns the factorial of a real

Returns the number of permutations of time

Returns the number of combinations of time

Returns a random number > 0 and < 1; to control a random number sequence, first store an integer seed value to

(random integer) Returns a random integer bound by the specified integers,

lower 

integer 

specify an integer > 1 for

(random normal) Returns a random real number from a normal distribution specified by random numbers, specify an integer > 1 for

(random binomial) Returns a random real number from a binomial distribution, where return a list of random numbers, specify an integer > 1 for

#ofSimulations

Œ '

randN randBi

upper

#ofTrials

mean

#ofTrials ‚

value

items

(

rand

) taken

(such as

number

0¶rand

; to return a list of random integers,

stdDeviation

and

; to return a list of

#ofTrials

1 and 0 

probabilityOfSuccess 

(r) at a

)

1; to

Chapter 3: Math, Calculus, and Test Operations

angle

can be a list for ¡ ,

DMS

and In a calculation, the result of

degrees'minutes'seconds

a entry is treated as degrees in

Degree

angle mode only. It is treated as radians in angle mode.

value

can sometimes be an expression, list, vector, or matrix. For details about specific syntax options and examples, refer to the A to Z Reference.

Radian

The MATH ANGLE Menu -

Œ (

NUM PROB ANGLE HYP MISC

or'4DMS

angle

degrees

angle

minutes'seconds

DMS

Overrides current angle mode setting to express

Designates an angle as

Displays

degrees

angle

in degrees¡minutes'seconds" format, even though you use

minutes'seconds

The MATH HYP (Hyperbolic) Menu -

NUM PROB ANGLE HYP MISC sinh cosh tanh sinh

value

sinh

value

cosh

value

tanh

value

sinh

value

cosh

value

tanh

cosh

Returns the hyperbolic sine of

Returns the hyperbolic cosine of

Returns the hyperbolic tangent of

Returns the hyperbolic arcsine of

Returns the hyperbolic arccosine of

Returns the hyperbolic arctangent of

degrees, minutes

to enter a DMS angle

Œ )

tanh

value

, and

angle

seconds

in degrees

in radians

Chapter 3: Math, Calculus, and Test Operations

value

can sometimes be an expression, list, vector, or matrix. For details about specific syntax options, refer to the A to Z Reference.

The MATH MISC (Miscellaneous) Menu -

NUM PROB ANGLE HYP MISC sum prod seq lcm gcd

list

sum

list

prod

expression,variable

seq(

end

Frac

step

[

begin

valueA,valueB

lcm(

valueA,valueB

gcd(

value

ercent%number

coefficientList,xValue

pEval(

‡

root

value

eval

]

)

Returns the sum of the elements of

Returns the product of the elements of

Returns a list in which each element is the value of evaluated for

variable

Returns the least common multiple of

Returns the greatest common divisor of

Displays

Returns

Returns the value of a polynomial (whose coefficients are given in

)

coefficientList

Returns the

value

as a fraction

value

divided by 100 (multiplied by .01)

percent

) at

xthroot

Returns a list of the values of all selected functions in the current graphing mode for the real

Œ *

Frac % pEval

begin

from

number

xValue

value

‡

list

expression

end

valueA

step

and

valueB

of the independent variable

eval

Chapter 3: Math, Calculus, and Test Operations

To interpolate y from the home screen, select from the enter

To interpolate x from the home screen, enter

inter(y1,x1,y2,x2,y)

You can store individual values with the (Chapter 2).

CATALOG

inter(x1,y1,x2,y2,x)

inter(

, and then

key

The InterpolateàExtrapolate Editor -

Œ / &

Using the interpolateàextrapolate editor, you can interpolate or extrapolate a value linearly, given two known pairs and the x-value or y-value of the unknown pair.



Display the interpolateàextrapolate editor.



Enter real values for the first known pair (x1,y1). The values can be expressions.



Enter values for the second known pair (x2,y2).



Enter a value for either the

value of the unknown pair.



If necessary, move the cursor to the value for which you want to solve (

Select

SOLVE



value or the

or y).

- Œ / &

The result is interpolated or extrapolated and displayed; the variables x and y are not changed. A solid square in the first column indicates the interpolated or extrapolated value.

After solving for a value, you can continue to use the interpolateàextrapolate editor.

Chapter 3: Math, Calculus, and Test Operations

You must set use the calculus functions.

evalF, nDer, der1

For

variable

der2

or complex number or list. You can use

expression

nDer

once in

fnInt, fMin

For

lower

Dec

can be a real

der1

. You can use

expression

, and

upper

must be true.

mode to

, and

and

der2

fMax

The CALC (Calculus) Menu

evalF nDer der1 der2 fnInt

- †

fMin fMax arc

The calculus functions return values with respect to any user-created variable, to built-in variables

expression,variable,value

evalF(

expression,variable ã,valueä

nDer(

expression,variableã,valueä

der1(

expression,variableã,valueä

der2(

expression,variable

fnInt(

lower,upper

expression,variable

fMin(

lower,upper

expression,variable

fMax(

lower,upper

expression,variable

arc(

start,end

eqn

)

and

)

, and to graphing variables such as x, t, and q.

exp

)

Returns the value of given variable

)

Returns an approximate numerical derivative of respect to

ariable

)

Returns the value of the first derivative of

variable

)

Returns the value of the second derivative of

variable

Returns the numerical integral of between

Returns the minimum value of between

Returns the maximum value of between

Returns the length of a segment of a curve defined by

variable

value

for the current variable value or specified variable

lower

with respect to

expression

value

for the current variable value or specified

upper

and

variable

upper

boundaries

between

with respect to

expression

start

and

with respect to

variable

expression

with respect to

with respect

with respect to

expression

end

for a

with

value

variable

Chapter 3: Math, Calculus, and Test Operations

Relational functions are valid for two lists of the same length. When

are lists, a list of

valueB

results calculated element by element is returned.

valueA

and

The built-in variable d defines the step size in calculating mode only) and

fMax(

, and

arc(

. The value of each must be >0. These factors affect the accuracy of the calculations. As example,

nDer(A^3,A,5)

arc(

. The built-in variable

becomes smaller, the approximation typically is more accurate. For

returns

75.0001

tol

defines the tolerance in calculating

=.01

, but returns 75 if

The function integral error value is stored to the variable

arc(

For

evalF(, der1(, der2(, fMin(, fMax(, nDer(, seq(

and

fnInt(

while

dxDer1

mode is set, these functions are not valid in

, and any equation variable, such as y1.

nDer(

fnIntErr

dxNDer

(in

=.0001

(Appendix).

differentiation

fnInt(, fMin(

expression

You can approximate the fourth derivative at the current value of x with this formula:

nDer(nDer(der2(x^4,x),x),x)

The TEST (Relational) Menu

= = < >

valueA

valueB



valueB

(equal to) Returns

valueB

(less than) Returns

valueB; valueA

(greater than) Returns greater than

(less than or equal to) Returns 1 if is not less than or equal to

- ˜

‚4ƒ

can be real or complex numbers, lists, vectors, matrices, or strings

and

valueB

valueB; valueA

is equal to

valueA

is less than

valueA

must be real numbers or lists

valueA

and

valueB

valueA

valueB; valueA

valueB

is greater than

must be real numbers or lists

is less than or equal to

and

valueB

; returns 0 if not equal;

; returns 0 if

valueB

must be real numbers or lists

valueA

; returns 0 if

valueB

valueA

is not less than

valueA

; returns 0 if

and

is not

valueA

Chapter 3: Math, Calculus, and Test Operations

You can use relational functions to control program flow (Chapter 16).

valueA‚valueB

valueA

valueB

(greater than or equal to) Returns

returns real numbers or lists

(not equal to) Returns

valueB; valueA

to matrices, or strings

valueA

is not greater than or equal to

valueA

valueB

and

valueA

is not equal to

can be real or complex numbers, lists, vectors,

is greater than or equal to

valueB; valueA

valueB

; returns 0 if

and

valueB

valueA

;

must be

is equal

Using Tests in Expressions and Instructions

The TI-86 Evaluation Operating System (Appendix) performs all operations except Boolean operators before it performs relational functions. For example:

The expression

♦

2+2==2+3

evaluates to 0. The TI-86 performs the addition first, and then

compares 4 to 5. The expression

♦

2+(2==2)+3

evaluates to 6. The TI-86 performs the test in parentheses

first, and then adds 2, 1, and 3.

Constants, Conversions,

Using Built-In and User-Created Constants .......................58

Converting Units of Measure............................................. 61

Number Bases.................................................................... 65

Using Complex Numbers ...................................................70

Bases, and Complex Numbers

M1 M2

F1 F2 F3

TI 86

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Using Built-In and User-Created Constants

A constant is a variable with a specific value stored to it. The common constants built into the TI-86. You cannot edit the value of a built-in constant.

You can create your own constants and add them to the user-created constant menu for easy access. To enter a user-created constant, you must use the user-created constant editor (page 60); you cannot use

to create a constant.

CONS BLTIN

menu items are

You can select built-in constants from the

CONS BLTIN

them using the keyboard and the

CHAR GREEK

menu or enter

menu.

The CONS (Constants) Menu -

BLTIN EDIT USER

built-in user-created constants menu constants menu

user-created constants editor

‘

The CONS BLTIN (Built-In Constants) Menu -

BLTIN EDIT USER

Na k Cc ec Rc

4m0H

‘ &

Gc g Me Mp Mn

0h c u

To use p, press select it from the

To use To use

, press

- ~

CATALOG

- ‚

- n ãE

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Built-In Constant Constant Name Constant Value

Na k Cc ec Rc Gc g Me Mp Mn

h c u

Avogadro's number 6.0221367E23 mole

Boltzman's constant 1.380658

Coulomb constant 8.9875517873682E9 N m

Electron charge 1.60217733

Gas constant 8.31451 Jàmole K

Gravitational constant 6.67259

Earth acceleration due to gravity 9.80665 màsec

Mass of an electron 9.1093897

Mass of a proton 1.6726231

Mass of a neutron 1.6749286

Permeability of a vacuum 1.2566370614359

Permittivity of a vacuum 8.8541878176204

Planck's constant 6.6260755

Speed of light in a vacuum 299,792,458 màsec

Atomic mass unit 1.6605402

Pi 3.1415926535898

Base of natural log 2.718281828459

11 N m

E E E

23 JàK

19 C

31 kg

27 kg

34 J sec

27 kg

6 NàA

12 Fàm

CONS USER

the names of all stored usercreated constants, arranged alphanumerically.

196.9665 is the atomic weight of gold (Au).

You can enter a value later.

If you select first constant name is displayed, or last constant name is displayed, the menu replaces the

EDIT

You also can delete a constant from the

DELET

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

menu items are

when the

CONS USER

menu.

CONS

MEM

screen.

Creating or Redefining a User-Created Constant



Display the



Display the constant editor. The prompt,

Value=

menu are displayed. ALPHA-lock is on.



Enter a constant name. Either enter a new name one to eight characters long, starting with a letter, or select a name from the The cursor moves to the

CONS EDIT



Enter the real or complex constant value, which can be an expression. The value is stored to the constant as you enter it. The user-created constant becomes a

The Constant Editor Menu -

PREV NEXT DELET

PREV NEXT

DELET

Displays the name and value (if any) of the previous constant on the

Displays the name and value (if any) of the next constant on the

Deletes the name and value of the constant currently displayed in the constant editor

menu. - ‘

CONS

Name=

prompt, and

CONS USER

Value=

prompt and the

menu.

menu is displayed (see below).

CONS USER

menu item.

‘ '

name

- n

196

9665

CONS USER

You can enter a conversion expression anywhere that an expression is valid.

In the example, Celsius is converted to degrees Fahrenheit. Always use parentheses when

value

degrees

is negative.

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Entering a Constant Name in an Expression

You can enter a constant in an expression in any of three ways.

♦

Select the constant name from the

♦

Select a user-created constant name from the

♦

Use the ALPHA keys, alpha keys, and other character keys to enter a constant name.

CONS BLTIN

menu or the

VARS CONS

CONS USER

screen.

menu.

Converting Units of Measure

With the TI-86, you can convert a value measured in one unit into its equivalent value in another unit of measure. For example, you can convert inches to yards, quarts to liters, or degrees Fahrenheit to degrees Celsius.

The units of measure from which and to which you convert must be compatible. For example, you cannot convert inches to degrees Fahrenheit, or yards to calories. Each menu item on the

LNGTH

(

), volume (

Converting a Unit of Measure

To use any conversion instruction, the syntax is:

value)currentUnit4newUnit

(



Enter the real



Display the



Select the

menu (page 62) represents a unit-of-measure group, such as length

CONV

VOL

), and pressure (

to be converted.

value

CONV

menu.

TEMP

conversion group.

PRESS

). Within each menu, all units are compatible.

D a

- ’ *





Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Select the current unit of measure ( conversion group menu. The unit abbreviation and conversion symbol ( 4 ) are pasted to the cursor location.

Select the new unit of measure ( conversion group menu. The unit abbreviation is pasted to the cursor location.



Convert the measurement.

) from the

The CONV (Conversions) Menu -

LNGTH AREA VOL TIME TEMP

length volume temperature speed force energy menu menu menu menu menu menu

Important:

and its negation sign, as in

area menu time menu mass menu pressure menu power menu

When you convert a negative value, you must enclose in parentheses the value

. Otherwise, the TI-86 order of evaluation will perform the

(L4)

’

MASS FORCE PRESS ENRGY POWER

SPEED

conversion first, and then apply the negation to the converted value.

If you enter... ...The TI-86 converts it to...

(L4)¡C4¡F

L4¡C4¡

24.8

degrees Fahrenheit (L4¡ Celsius converted to degrees Fahrenheit)

39.2

degrees Fahrenheit (4¡ Celsius converted to degrees Fahrenheit, then negated)

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

The CONV LNGTH (Length) Menu -

mm cm m in ft

millimeters centimeters meters inches feet

The CONV AREA Menu -

ft m mi

square feet

square meters

square miles

yd km mile nmile lt-yr

’ '

km acre

The CONV VOL (Volume) Menu -

liter gal qt pt oz

liters gallons quarts pints ounces

The CONV TIME Menu -

sec mn hr

seconds minutes hours

m cup

’ )

day yr week

’ &

yards kilometers miles nautical miles light-years

square kilometers acres square inches

’ (

cubic centimeters cubic inches cubic feet cubic meters cups

days years weeks

The CONV TEMP (Temperature) Menu -

degrees Celsius

degrees Fahrenheit

’ *

degrees Kelvin

mil

mils

Ang

Angstroms

fermi

fermis

rod

rods

fath

fathoms

square centimeters

square yards

hectares

tsp

teaspoons

tbsp

tablespoons

milliliters

galUK

UK gallons

ozUk

UK ounces

milliseconds

microseconds

nanoseconds

degrees Rankin

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

The CONV MASS Menu -

gm kg lb

grams kilograms pounds

The CONV FORCE Menu -

N dyne

Newtons dynes

’ / &

amu

atomic mass units

slug

slugs

’ / '

tonf

ton force

kgf

kilogram force

The CONV PRESS (Pressure) Menu -

atm bar Nàm

atmospheres bars

Newtons per square meter

lbàin

pounds per square inch

mmHg

millimeters of mercury

mmH

millimeters of water

The CONV ENRGY (Energy) Menu -

J cal Btu

oules calories British thermal units

The CONV POWER Menu -

hp W

horsepower Watts

The CONV SPEED Menu -

ftàs màs

feet per second meters per second

ft-lb

foot-pounds

kw-hr

kilowatt hours

electron Volts

’ / *

ftlbàs calàs

foot-pounds per second calories per second per minute

’ / / &

miàhr

miles per hour

kmàhr

kilometers per hour

’ / (

’ / )

ton

tons

mton

metric tons

lbf

pound force

inHg

inches of mercury

inH2O

inches of water

erg

ergs

l-atm

liter-atmospheres

Btuàm

British thermal units

knot

knots

To enter a forward slash

, you can use the F key

(

)

or paste it from the

CATALOG

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Converting a Value Expressed as a Rate

To convert a value expressed as a rate on the home screen, you can use parentheses and

the division operator (

). For example, if a car travels 325 miles in 4 hours, and you want

to know the rate of speed in kilometers per hour, enter this expression:

(325à4)miàhr4kmàhr

This expression returns

131

kmàhr (rounded up).

You also can return this result using only a forward slash, as in:

325mile4kmà4hr4hr

Number Bases

The number base mode setting (Chapter 1) controls how the TI-86 interprets an entered number and displays results on the home screen. However, you can enter numbers in any number base using number base designators Ü, Ý, Þ, and ß. Then you can display the result on the home screen in any number base using number base conversions.

All numbers are stored internally as decimal. If you perform an operation in a mode setting

Dec

other than calculation and expression.

For example, in

, the TI-86 performs integer mathematics, truncating to an integer after every

Hex

mode,

1à3+7

returns 7h (1 divided by 3, truncated to 0, and then added to 7).

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Number Base Ranges

Binary, octal, and hexadecimal numbers on the TI-86 are defined in these ranges.

Type Low ValueàHigh Value Decimal Equivalent

Binary 1000 0000 0000 0001

0111 1111 1111 1111

Octal 5120 6357 4134 0001

2657 1420 3643 7777

Hexadecimal

ÚÚÚÚ Õ50× ÙÚ

0000 5ÕÚ3 107Õ 3

One’s and Two’s Complements

To obtain the one's complement of a binary number, enter the the number. For example,

not 111100001111

To obtain the two's complement of a binary number, press a before entering the number. For example,

111100001111

mode returns

Bin

85 ×001

ÚÚÚ

b b

o o

h h

mode returns

Bin

1111000011110001

32,767

99,999,999,999,999

function (page 68) before

not

1111000011110000

The (Number) BASE Menu -

Õ-Ú

hexadecimal base conversion rotateàshift characters menu menu menu base type Boolean operator

TYPE CONV BOOL BIT

menu menu

—

menu items and

BASE ÕBASE TYPE

not the same as regular alphabetical characters.

menu items are

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

The BASE Õ-Ú (Hexadecimal Characters) Menu -

This is the

BASE Õ-

ЦЧШЩЪ

menu displayed on the home screen. To use Õ, press

TYPE CONV BOOL BIT

— &

- e

In the example, the upper menu is the list editor menu

- ”

( base mode).

If not set, you must enter the designator, even if the number contains a special hexadecimal character.

Dec

number

Hex

number base mode is

When an editor menu is the upper menu, Õ and ...Õ and Ö move to two separate cells, and Ù and

are combined in one cell. If you press & or /... are combined. To switch back, press * or /.

{ } NAMES " OPS { } NAMES " OPS

Õ-Ö× Ø Ù Ú

ХЦЧШЩ

Entering Hexadecimal Digits

To enter a hexadecimal number, use the number keys as you would for a decimal number.

Select the hexadecimal characters Õ through Ú from the menu as needed.

The BASE TYPE Menu -

Õ-Ú

TYPE

CONV BOOL BIT

— '

ÜßÝÞ

In an expression, you can designate a number in any number base, regardless of mode. After you enter the number, select the appropriate base type symbol from the menu. The base type symbol is pasted to the cursor location. Here are some examples.

Dec

Bin

mode (default):

mode:

10Ü+10 10ß+10

10ß+10 10Þ+10

b b

10010

1100

12 26

Oct

mode:

10Ü+10 10Þ+10

Hex

mode:

10Ü+10 10Þ+10

b b

BASE TYPE

Õß

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

value

can be an expression, list, vector, or matrix. For detailed syntax descriptions, refer to the A to Z Reference.

The BASE CONV (Conversion) Menu -

Õ-Ú

value value

Bin

TYPE CONV BOOL BIT

Bin

Hex

Displays Displays

Oct

value

as binary

value

as hexadecimal

Dec

Converting Number Bases



mode, solve









Dec

Add

to the result and convert it to

Add

to the result and convert it to

Add

to the result and convert it to

Add

to the result and convert it to

10Ü + Úß + 10Ý + 10

The BASE BOOL (Boolean) Menu -

Õ-Ú

and or xor not

valueA

TYPE CONV BOOL BIT

valueB valueA or valueB valueA

and

number base display.

Bin

number base display.

Hex

number base display.

Oct

number base display.

Dec

— )

— (

value value

Oct

Dec

Displays Displays

valueB

xor

value

as octal

value

as decimal

10Ü+Úß+10Ý+10 Ans+14Bin Ans+14Hex Ans+14Oct Ans+1

not

value

100100

Both the argument and the result must be within defined number ranges (page 66).

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Results of Boolean Operations

When a Boolean expression is evaluated, the arguments are converted to hexadecimal integers and the corresponding bits of the arguments are compared, as this table shows.

Results

valueA

is... ...and

1 1 1100 1 0 0110 0 1 0111 0 0 0001

valueB

is...

and or xor not

valueA

(

The result is displayed according to the current mode setting. For example:

♦

Bin

mode,

101 and 110

returns

100Ü

Hex

♦

mode,

5 and 6

returns 4ß.

)

Rotate and shift operate on 16 base digits. To minimize an overflow error, enter the argument in binary form.

The BASE BIT Menu -

Õ-Ú

rotR rotL shftR shftL

TYPE CONV BOOL BIT

value

Rotates Rotates Shifts Shifts

value

value value value

right

left right left

— *

Variable names with complex numbers stored to them are listed on the screen (Chapter 2).

Lists, matrices, and vectors can have complex elements.

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

VARS CPLX

Using Complex Numbers

A complex number has two components: real (a) and imaginary (+bi). On the TI-86, you enter the complex number a+bi as:

real,imaginary

(

♦

You can enter a complex number in rectangular or polar form, regardless of the current complex number mode setting. The separator (

♦

To enter rectangular form, separate

♦

To enter polar form, separate

)

in rectangular form

magnitude

real

(

♦

magnitude±angle) in polar form

or ± ) determines the form.

imaginary

and

angle

with a comma (P).

with an angle symbol (- ).

The graph format settings

RectGC

(Chapter 5) determine the complex number form of graph screen coordinates.

and

PolarGC

Each component (

real, imaginary, magnitude

expression that evaluates to a real number; expressions are evaluated when you press

RectC

When

complex number mode is set, complex

, or

angle

) can be a real number or an

numbers are displayed in rectangular form, regardless of the form in which you enter them (as shown to the right).

PolarC

When

complex number mode is set, complex numbers are displayed in polar form, regardless of the form in which you enter them (as shown to the right).

Complex Results

Complex numbers in results, including list, matrix, and vector elements, are displayed in the form (rectangular or polar) specified by the mode setting (Chapter 1) or by a display conversion instruction (page 61).

♦ ♦

When When

Radian

angle mode is set, results are displayed as

Degree

angle mode is set, results are displayed as

magnitude±angle

(

real,imaginary

(

)

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

You can enter the name or a complex list, vector, or matrix as an argument for any menu item.

CPLX

For example, when

(1.32565429614±12.7643896828)

PolarC

and

Degree

modes are set,

(2,1)N(1±45)

returns

Using a Complex Number in an Expression

♦

Enter the complex number directly.

♦

Use the ALPHA keys, alpha keys, and other character keys to enter a complex variable.

♦

Select a complex variable from the

VARS CPLX

The CPLX (Complex Number) Menu -

conj real imag abs angle

conj (real,imaginary)

conj (magnitude real (real,imaginary)

real (magnitude imag (real,imaginary)

imag (magnitude abs (real,imaginary)

abs (magnitude

angle)

Returns the complex conjugate of a complex value, list, vector or matrix; the result is

Returns

(magnitude

Returns the real portion of a complex number, list, vector, or matrix as a real number; the result is

Returns

magnitude

Returns the imaginary (non-real) portion of a complex number, list,

ector, or matrix as a real number; the result is

Returns

magnitude

(Absolute value) Returns the magnitude (modulus) of a complex number, list, vector, or matrix of complex numbers; the result is

‡(real

Returns

imagi nary

magnitude

‹

4 4

(real,

±L

angle)

cosine(

sine(

)

screen.

Rec

imaginary)

real

angle

)

angle

)

Pol

imaginary

Chapter 4: Constants, Conversions, Bases, and Complex Numbers

Select { and } from the menu.

You must enter commas to separate list elements.

LIST

angle (real,imaginary)

Rec

angle)

angle (magnitude

complexValue

Returns the polar angle of a complex number, list, vector, or matrix calculated as quadrant or

Returns

Displays

angle

complexValue

tan

(imaginary

in the third quadrant); the result is tan

(where

real)

p<anglep

(adjusted by p in the second

)

in rectangular format

imaginaryàreal

(

(real,imaginary)

regardless of complex mode setting; valid only at the end of a command

complexValue

is indeed complex

in polar format (

magnitude

angle

), regardless

complexValue

Pol

and only when

Displays of complex mode setting; valid only at the end of a command and only

complexValue

when

is indeed complex

You can enter a complex list, vector, or matrix directly. The syntax below is for lists. To enter a complex vector or matrix, substitute brackets for braces below and use the correct form for either data type (Chapters 12 and 13).

In rectangular form, to use lists of complex numbers with

conj, real, imag, abs

, and

angle

, the

syntax is:

realA,imaginaryA

conj{(

In polar form, to use lists of complex numbers with

realB,imaginaryB

),(

realC,imaginaryC

),(

conj, real, imag, abs

...

}

, and

angle

, the

syntax is:

magnitudeA±angleA

real{(

magnitudeB±angleB

),(

magnitudeC±angleC

),(

...

}

When you use a list the TI-86 calculates the result element by element and returns a list, in which each element is expressed according to the complex mode setting.

)

Defining a Graph................................................................ 74

Setting the Graph Mode ....................................................74

The GRAPH Menu .............................................................. 75

Using the Equation Editor.................................................. 76

Setting the Window Variables ...........................................81

Setting the Graph Format ..................................................83

Displaying a Graph ............................................................85

Function Graphing

M1 M2

F1 F2 F3

TI 86

Chapter 5: Function Graphing

Some of these steps are not necessary every time you define a graph.

Defining a Graph

This chapter describes the process for graphing functions in process is similar for each TI-86 graphing mode. Chapters 8, 9, and 10 describe the unique aspects of polar, parametric, and differential equation graphing modes. Chapter 6 describes various graphing tools, many of which you can use in all graphing modes.



Set the graphing mode (page 74).



Define, edit, or select one or more functions in the equation editor (pages 76 and 77).



Select the graph style for each function (page 79).



Deselect stat plots, if necessary (page 81).



Set the viewing window variables (page 81).



Select the graph format settings (page 83).

Func

graphing mode, but the

Setting the Graph Mode

To display the mode screen, press -

Func

settings, including

graphing mode, are highlighted in the

icture to the right. The graphing modes are on the fifth line.

Func

♦ ♦ ♦ ♦

(function graphing)

Pol

(polar graphing; Chapter 8)

Param

(parametric graphing; Chapter 9)

DifEq

(differential equation graphing; Chapter 10)

. All default mode

Chapter 1 describes all mode settings in detail.

Chapter 5: Function Graphing

Each graphing mode has a unique equation editor. You must select the graphing mode and

Dec

number base mode before you enter the functions. The TI-86 retains in memory all

equations stored to the

Func, Pol, Param

, and

DifEq

equation editors. Each mode also has

unique graph format settings and window variables.

Stat plot onàoff status, zoom factors, mode settings, and tolerance apply to all graphing modes; changing the graphing mode does not affect them.

These mode settings affect graphing results.

♦ ♦

Radian dxDer1

or or

Degree

angle mode affects the interpretation of some functions.

dxNDer

differentiation mode affects plotting of selected functions.

Chapter 6 describes these

menu items:

GRAPH

ZOOM, TRACE, MATH DRAW, STGDB, RCGDB EVAL, STPIC

, and

RCPIC

The GRAPH Menu

y(x)= WIND ZOOM TRACE GRAPH

y(x)= WIND ZOOM TRACE

GRAPH MATH DRAW

Displays the equation editor; use this screen to enter functions to be graphed

Displays the window editor; use this editor to change graph screen dimensions

Displays the

Activates the trace cursor; use this cursor to trace along the graph of a specific function

Displays the graph screen; graphs all selected functions and turned on stat plots

Displays the

GRAPH ZOOM

GRAPH MATH GRAPH DRAW

MATH DRAW FORMT STGDB RCGDB

EVAL STPIC RCPIC

menu; use these items to change the graph screen dimensions

menu; use this menu to explore graphs mathematically

menu; use this menu to draw on graphs or test pixels

Chapter 5: Function Graphing

FORMT STGDB RCGDB EVAL STPIC RCPIC

Displays the graph format screen; use this screen to select graph format settings

Displays the

Name=

prompt and

Name=

prompt and

Eval x=

prompt; enter an x for which you want to solve the current function

Name=

prompt and

Name=

prompt and

STGDB

menu; use this prompt to enter a

RCGDB

STPIC RCPIC

menu; use this menu to recall a graph database

menu; use this prompt to enter a

menu; use this menu to recall a picture

GDB

PIC

variable

Using the Equation Editor

To display the equation editor in

y(x)=

from the

GRAPH

menu (

6 &

shifts up and the equation editor menu is displayed as the lower menu. You can store up to 99 functions in the equation editor, if sufficient memory is available.

If a function is selected, its equals sign (=) is highlighted in the equation editor. If the function is deselected, its equals sign is not highlighted. Only selected functions are plotted when the TI-86 plots a graph.

The Equation Editor (GRAPH y(x)=) Menu

y(x)= WIND ZOOM TRACE GRAPH

x y INSf DELf SELCT

graphing mode, select

Func

GRAPH

). The

6 &

ALL+ ALLNSTYLE

Chapter 5: Function Graphing

To move from the first equation editor function to the last, press

To move to the beginning or end of an equation, press

- !

An ellipsis indicates that an equation continues beyond the screen.

- "

x y INSf

Pastes the variable x to the current cursor location (same as 2 or - n

Pastes the variable y to the current cursor location (same as - n

Inserts a deleted equation variable (function) name above the current cursor location (only the variable name is inserted)

DELf SELCT ALL+

ALL STYLE

Deletes the function that the cursor is on

Changes the selection status of the function that the cursor is on (selects or deselects)

Selects all defined functions in the equation editor

Deselects all defined functions in the equation editor

Assigns the next of seven available graph styles to the function that the cursor is on

Defining a Function in the Equation Editor



Display the equation editor.



If functions are stored in the equation editor, move the cursor down until a blank function is displayed.



Enter an equation in terms of function. When you enter the first character, the function is selected automatically. (The function’s equals sign is highlighted.)



Move the cursor to the next function.

to define the

6 &

( # or b )

= 2

b or #

)

Chapter 5: Function Graphing

You can edit expressions you inserted using

Rcl

Notes about Defining Function Equations

♦

You can include functions, variables, constants, matrices, matrix elements, vectors, vector elements, lists, list elements, complex values, or other equations in the equation.

♦

If you include matrices, vectors, or complex values, the equation must evaluate to a real number at each point.

♦

You can include another defined function in an equation. For example, given

y2=4+y1

and

♦

To enter a function name, select

, the function y2 would equal 4 plus the sine of x.

from the equation editor menu, and then enter the

y1=sin x

appropriate number.

♦

To insert the contents of an equation variable, use

Rcl

equation variable at the

prompt, use the ALPHA keys, alpha keys, and other

RCL

(Chapter 1). To enter the

character keys.

♦

To select all functions from the home screen or in the program editor, select

CATALOG

the

♦

To select specific functions from the home screen or in the program editor, select from the function, and press

♦

To deselect functions from the home screen or in the program editor, use same way you use

♦

When a function evaluates to a non-real number, the value is not plotted on the graph;

(or enter the individual characters) and press

CATALOG

(or enter the individual characters), enter the number of each

. For example, to select

FnOn

to select functions.

y1, y3

, and y5, enter

FnOn 1,3,5

FnOn

FnOff

no error is returned.

the

from

FnOn

The TI-86 graphs all selected

functions on the same graph screen.

(shade above) and

(shade below) are availabl

Func

only in

(dot) is available in all

graphing modes except

DifEq

graphing mode.

Chapter 5: Function Graphing

Selecting Graph Styles

Depending on which graphing mode is set, the TI-86 offers up to seven distinct graph styles. You can assign these styles to specific functions to visually differentiate each from the others.

For example, you can show

Ây2=

dotted line (

), and shade the area above y3 (

as a connected line (

¾y3=

»y1=

in the equation editor) and y2 as a

Also, you can manipulate the styles to illustrate actual phenomena graphically, such as a ball flying through the air (using Á) or the circular movement of a chair on a Ferris wheel (using À).

Icon Style Characteristics of the Plotted Function

» ¼ ¾ ¿ À Á Â

Line Thick Above Below Path Animate Dot

A solid line connects each plotted point; this is the default in

A thick solid line connects each plotted point

Shades the area above the function

Shades the area below the function

A circle cursor traces the leading edge of the function and draws a path as it plots

A circle cursor traces the leading edge of the function as it plots; does not draw a path

A small dot represents each plotted point; this is the default in

To set the graph style from a program, select

GrStl(

from the

CATALOG

Connected

Dot

mode

(A to Z Reference).

Chapter 5: Function Graphing

In the example, above) is selected for window variables are set to the default values (page 82).

(shade

. All

Setting the Graph Style in the Equation Editor



Display the equation editor.



Move the cursor to the function or functions for which you want to set the graph style.



Display the equation editor menu item

Select

STYLE

repeatedly to scroll the graph



style icons to the left of the equation name.

STYLE

6 &

( (

If you assign function that graphs a family of curves (page 86), the same pattern rotation applies to the members of the family of curves.

to a



View the graph with the new graph style.



Clear the

GRAPH

menu to view the graph only.

- *

Using Shading Patterns to Differentiate Functions

When you select ¾ (shade above) or ¿ (shade below) for more than one function, the TI-86 rotates through a series of four shading patterns.

First shaded function: vertical lines

♦

Second shaded function: horizontal lines

♦

Third shaded function: negatively sloping diagonal lines

♦

Fourth shaded function: positively sloping diagonal lines

♦

The rotation returns to vertical lines for the fifth shaded function and repeats the order.

Chapter 5: Function Graphing

Viewing and Changing OnàOff Status of Stat Plots

Plot1 Plot2 Plot3

on the top line of the equation editor displays the onàoff status of each stat

plot (Chapter 14). When a plot name is highlighted on this line, the plot is on.

To change the onàoff status of a stat plot from the equation editor, press $, ", and ! to place the cursor on

Plot1, Plot2

, or

Plot3

, and then press

Setting the Window Variables

The graph screen window represents the portion of the coordinate plane displayed on the graph screen. By setting window variables, you can define the graph screen window boundaries and other attributes.

To remove tick marks from both axes, set

yScl=0

Small graph resolution but may cause the TI-86 to plot graphs more slowly

xScl=0

xRes

values improve

and

xMin, xMax, yMin

(x scale) is the number of units represented by the distance from one tick mark to the next

xScl

, and

are the graph screen boundaries.

yMax

tick mark on the x-axis.

(y scale) is the number of units represented by the distance from one tick mark to the

yScl

next tick mark on the y-axis.

sets pixel resolution for function graphs only, using integers 1 through 8.

xRes

♦ ♦

At At

(the default), functions are evaluated and graphed at each pixel on the x-axis.

xRes=1

, functions are evaluated and graphed at every eighth pixel along the x-axis.

xRes=8

Chapter 5: Function Graphing

xMin<xMax

both must be true to graph successfully.

In the example, changed to

and

yMin<yMax

yMin

Displaying the Window Editor

To display the window editor, select menu (

6 '

). Each graphing mode has a unique

WIND

from the

GRAPH

window editor. The window editor to the right shows the

Func

default values in

xRes=1

(x resolution) is below

graphing mode. $ indicates that

yScl

on the window editor.

Changing a Window Variable Value



Display the window editor.



Move the cursor to the window variable you want to change.



Edit the value, which can be an expression.



Evaluate any expressions and store the value.

6 '

# # #

To change a window variable value from the home screen or in the program editor, enter the value, and then press screen ( -

w / /

. Either select the window variable from the

WIND

) or enter individual characters. Press

VARS WIND

Chapter 5: Function Graphing

Setting Graphing Accuracy with @x and @y

The window variables

and

define the distance from the center of one pixel to the center of any adjacent pixel. When you display a graph, the values of calculated from

xMin+xMax

xMin, xMax, yMin

)à126

, and

yMax

using these formulas:

yMin+yMax

)à62

and

are

The TI-86 retains independent format settings for each graphing mode.

DifEq

graphing mode, the

In graph format screen key sequence is (Chapter 10).

6 / &

and

are not on the window editor. To change them, you must follow the steps above for changing a window variable value from the home screen or in the program editor. When you change the values stored to

yMax

from

xMin

, and

yMin

, and the new values are stored.

and

, the TI-86 automatically recalculates

xMax

and

Setting the Graph Format

To display the graph format screen, select

GRAPH

menu (

6 / (

). The graph format settings define various characteristics of the displayed graph. The current settings are highlighted.

To change a setting, move the cursor onto the new setting, and then press

, the same as on the mode screen.

FORMT

from the

Chapter 5: Function Graphing

DifEq

graphing mode has a unique set of graph format settings (Chapter 10).

Grid points cover the graph screen in rows that correspond to the tick marks on each axis.

RectGC

PolarGC

CoordOn CoordOff DrawLine DrawDot

SeqG

SimulG

GridOff GridOn AxesOn AxesOff

LabelOff LabelOn

Displays the cursor location as rectangular graph coordinates x and y; when

RectGC

is set, plotting the graph, moving the free-moving cursor, and tracing update x and y; if

CoordOn

Displays the cursor location as polar graph coordinates R and q; when plotting the graph, moving the free-moving cursor, and tracing update

CoordOn

format also is selected, x and y are displayed

format also is selected, R and q are displayed

PolarGC

x, y, R

is set,

and q; if

Displays the cursor coordinates at the bottom of the graph

Does not display the cursor coordinates at the bottom of the graph

Draws a line between the points calculated for the functions in the equation editor

Plots only the calculated points for the functions in the equation editor (sequential graphing) Evaluates and plots one function completely before evaluating

and plotting the next function

(simultaneous graphing) Evaluates and plots all selected functions for a single value

and then evaluates and plots them for the next value of

Omits the grid points from the display

Displays grid points

Displays the axes

Omits the axes from the display;

AxesOff

overrides the

LabelOffàLabelOn

format

setting

Omits the axis labels from the display

Labels the axes, if various labels in

AxesOn

DifEq

is also selected; x and y for

mode

Func, Pol

, and

Param

modes;

In the example graph to the right, all default settings related to graphing are set.

To view the graph without the

menu on the bottom

GRAPH

line, press plotting the graph.

When you pause, the busy indicator in the top-right corner becomes a dotted line.

after

Chapter 5: Function Graphing

Displaying a Graph

To display a graph, select from the

GRAPH

menu. The graph screen is displayed. If the graph is newly defined, the busy indicator is displayed at the top-right corner as the TI-86 draws the graph.

SeqG

format, the TI-86 draws each selected function one by one, in function-name

♦

order (for example, In

SimulG

format, the TI-86 draws all selected graphs simultaneously.

♦

You can display and explore a graph from a program (Chapter 16). To use graphing commands on the home screen, select them from the

Pausing or Stopping a Graph in Progress

♦

To pause graph plotting, press

♦

To stop graph plotting, press ^. To replot, select

Modifying a Drawn Graph

To remove these items from the graph screen: Press (or select):

Cursor, coordinate values, or menus (To restore menus, press . or

Free-moving cursor and coordinate values but not the menus

Cursor and coordinate values but not the menus

GRAPH

is graphed first, y2 is graphed second, and so on).

CATALOG

. To resume plotting, press

or entering the individual characters.

GRAPH

from the

again.

GRAPH

)

b 6

menu.

GRAPH

Chapter 5: Function Graphing

When you use more than one list in an expression, all lists must have the same dimension.

Graphing a Family of Curves

If you enter a list as an element in an equation, the TI-86 plots the function for each value in the

SimulG

list, graphing a family of curves. In

graphing order mode, the TI-86 graphs all functions

sequentially for the first element in each list, then for the second element, and so on.

For example,

{2,4,6} sin x

graphs

three functions:

2 sin x, 4 sin x

, and

6 sin x

The equation

{2,4,6} sin ({1,2,3} x)

also graphs three functions:

2 sin x, 4 sin (2x)

, and

6 sin (3x)

Smart Graph

Smart Graph displays the previously displayed graph when you press

, as long as all factors that would cause replotting are unchanged since the graph was last displayed. Smart Graph replots if you performed any of these actions since the graph was last displayed.

♦

Changed a mode setting that affects graphs

♦

Changed a function or stat plot that was plotted on the last graph screen

♦

Selected or deselected a function or stat plot

♦

Changed the value of a variable in a selected function

♦

Changed the value of a window variable setting

♦

Changed a graph format setting

Graph Tools on the TI-86................................................... 88

Tracing a Graph ................................................................. 90

Resizing the Graph Screen with ZOOM Operations ...........91

Using Interactive Math Functions ...................................... 95

Evaluating a Function for a Specified x............................ 101

Drawing on a Graph ........................................................101

Graph Tools

M1 M2

F1 F2 F3

TI 86

Chapter 6: Graph Tools

Graph Tools on the TI-86

Chapter 5 describes how to use the

GRAPH

define and display the graph of a function in to use the other

menu items to apply preset graph screen dimensions, explore the

GRAPH

menu items

Func

y(x)=, WIND, GRAPH

graphing mode. This chapter describes how

graph and trace specific functions, perform mathematical analyses, draw on graphs, and store and recall graphs and drawings. You can use most graph tools in all four graphing modes.

, and

FORMT

This is the

Func

graphing mode. The

menu differs slightly

GRAPH

from graphing mode to graphing mode.

GRAPH

menu in

The GRAPH Menu

y(x)= WIND ZOOM TRACE GRAPH

ZOOM TRACE MATH DRAW STGDB RCGDB EVAL

Displays the

Activates the trace cursor; use this cursor to trace along graphs of specific functions

Displays the

GRAPH ZOOM

GRAPH MATH GRAPH DRAW

Name=

prompt and

Name=

prompt and

Eval x=

menu; use these items to apply preset graph screen dimensions

menu; use this menu to explore graphs mathematically

menu; use this menu to draw on graphs

prompt; use this prompt to enter an x value for which you want to

solve the current function

STPIC RCPIC

Displays the

Name= Name=

prompt and

MATH DRAW FORMT STGDB RCGDB

EVAL STPIC RCPIC

GDB

menu; use this prompt to enter a

GDB

menu; use this menu to recall a

PIC

menu; use this prompt to enter a

PIC

menu; use this menu to recall

PIC

GDB

variable

PIC

variable

Texas Instruments TI-86 User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Table of Contents

TI-86 Quick Start 1

Chapter 1: Operating the TI-86 15

Chapter 2: The CATALOG, Variables, and Characters 37

Chapter 3: Math, Calculus, and Test Operations 47

Chapter 4: Constants, Conversions, Bases, and Complex Numbers 57

Chapter 5: Function Graphing 73

Chapter 6: Graph Tools 87

Chapter 7: Tables 109

Chapter 8: Polar Graphing 115

Chapter 9: Parametric Graphing 123

Chapter 11: Lists 151

Chapter 12: Vectors 167

Chapter 13: Matrices 177

Chapter 14: Statistics 187

Chapter 15: Equation Solving 201

Chapter 16: Programming 213

Chapter 17: Memory Management 229

Chapter 18: The TI-86 Communication Link 233

Chapter 19: Applications 243

Chapter 20: A to Z Function and Instruction Reference 261

Appendix 379

Index

TI-86 Quick Start

Preparing to Use Your New TI-86

Installing the AAA Batteries

Turning On and Turning Off the TI-86

Adjusting the Contrast

Resetting All Memory and Defaults

Calculating on the Home Screen

Calculating the Sine of a Number

Storing the Last Answer to a Variable

Using a Variable in an Expression

Editing an Expression

Displaying a Complex Number as a Result

Using a List with a Function

Displaying the Integer Part of Real Numbers in a List

Removing (Exiting) a Menu

Finding the Square Root

Calculating Derivatives

Retrieving, Editing, and Re-evaluating the Previous Entry

Converting Degrees Fahrenheit to Degrees Celsius

Storing an Unevaluated Expression to an Equation Variable

Plotting Functions on the Graph Screen

Displaying and Entering Functions in the Equation Editor

Changing the Graph Style of a Function

Plotting a Function on the Graph Screen

Tracing a Function

Evaluating y for a Specific x Value (During a Trace)

Changing a Window Variable Value

Deselecting a Function

Zooming In on a Portion of the Graph Screen

Installing or Replacing Batteries

When to Replace Batteries

Turning On and Turning Off the TI-86

Adjusting the Display Contrast

The Home Screen

Displaying Entries and Answers

Entering Numbers

Entering Negative Numbers

Using Scientific or Engineering Notation

Entering Complex Numbers

Entering Other Characters

The 2nd Key

The ALPHA Key

ALPHA-lock and alpha-lock

Common Cursors

Cursor Direction Keys

Inserting, Deleting, and Clearing Characters

Entering Expressions and Instructions

Entering an Expression

Using Functions in Expressions

Using an Instruction

Entering Functions, Instructions, and Operators

Entering Consecutive Entries

The Busy Indicator