Texas Instruments TI-80 User Manual

TI-80

GRAPHING CALCULATOR

GUIDEBOOK

TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated.

Windows is a registered trademark of Microsoft Corporation. Macintosh is a registered trademark of Apple Computer, Inc.

Important

US FCC Information Concerning Radio Frequency Interference

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

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

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

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

• Reorient or relocate the receiving antenna.

• Increase the separation between the equipment and receiver.

• Connect the equipment into an outlet on a circuit different

from that to which the receiver is connected.

• Consult the dealer or an experienced radio/television

technician for help.

Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment.

This manual describes how to use the TI.80 Graphing Calculator. Getting Started gives a quick overview of its features. The first chapter gives general instructions on operating the TI.80. Other chapters describe its interactive features. The applications in Chapter 11 show how to use these features together.

Getting Started: Do This First!

Chapter 1: Operating the TI-80

Using this Guidebook Effectively Glossary

TI-80 Keyboard First Steps TI-80 Menus

.........................................

...................................

.......................................

......................................

....................

Entering a Calculation: Compound Interest Continuing a Calculation Defining a Function: Box with Lid Defining a Table of Values Zooming In on the Table Changing the Viewing Window Displaying and Tracing the Graph Zooming In on the Graph Other TI-80 Features

Turning the TI-80 On and Off Setting the Display Contrast The Display

......................................

Entering Expressions and Instructions The Edit Keys Setting Modes TI-80 Modes Variable Names

....................................

......................................

...................................

Storing and Recalling Variable Values Last Entry Last Answer TI-80 Menus The

........................................

......................................

and

VARS

Y-VARS

EOS (Equation Operating System) Error Conditions

...........................

...................

..........................

...........................

......................

...................

...........................

..............................

.......................

........................

...............

................

......................

Menus

..................

.................................

...........

viii

xii

2 3 4 5 6 7 8

9 11 12 13 14

1-2 1-3 1-4 1-6 1-8

1-9 1-10 1-12 1-13 1-14 1-16 1-17 1-19 1-20 1-22

Introduction iii

Chapter 2: Math, Angle, and Test Operations

Getting Started: Lottery Chances Using the TI-80 Functions Keyboard Math Operations

MATH MATH MATH NUM MATH PRB ANGLE TEST

Operations

(Number) Operations

(Probability) Operations

Operations

(Relational) Operations

..........................

.........................

...........................

................................

.......................

....................

...................

.................

2-2

2-3

2-4

2-7 2-10 2-12 2-14 2-16

Chapter 3: Fractions

Chapter 4: Function Graphing

Chapter 5: Parametric Graphing

Getting Started: Working with Fractions Setting Modes for Fraction Results Entering and Using Fractions in Calculations The

FRACTION

..............................

Getting Started: Graphing a Circle Defining a Graph Setting Graph Modes Defining Functions in the Evaluating Selecting Functions Defining the Viewing Window Displaying a Graph

..................................

..............................

List

Functions in Expressions

...............................

......................

................................

.............

..................

.........

...................

....................

.............

Exploring a Graph with the Free-Moving Cursor Exploring a Graph with Exploring a Graph with Setting the Zoom Factors

Getting Started: Path of a Ball Defining and Displaying a Parametric Graph Exploring a Parametric Graph

.....................

TRACE

......................

ZOOM

..........................

......................

..........

......................

......

3-2

3-4

3-6

3-8

4-2

4-3

4-4

4-5

4-7

4-8

4-9 4-11 4-12 4-13 4-15 4-18

5-2

5-3

5-6

iv Introduction

Chapter 6: Tables

Getting Started: Roots of a Function Defining the Independent Variable Defining the Dependent Variable Displaying the Table

...............................

....................

.................

..................

6-2

6-3

6-4

6-5

Chapter 7: Draw Operations

Chapter 8: Lists

Chapter 9: Statistics

Getting Started: Shading a Graph

...............................

DRAW DRAW

Drawing Lines

....................................

Drawing Horizontal and Vertical Lines Drawing a Function

...............................

Shading Areas on a Graph Drawing Points Clearing a Drawing

...................................

................................

Getting Started: Generating a Sequence About Lists

LIST OPS LIST MATH

.......................................

Operations

..............................

............................

....................

...............

..........................

..............

Getting Started: Building Height and City Size Setting Up a Statistical Analysis The

STAT

List Editor

..............................

Viewing, Entering, and Editing Lists Sorting and Clearing Lists Statistical Analysis

................................

Types of Statistical Analysis Statistical Variables Statistical Plotting

...............................

................................

Statistical Analysis in a Program Statistical Plotting in a Program

.....................

.................

..........................

........................

....................

.....................

.........

7-2

7-3

7-4

7-5

7-6

7-7 7-10 7-12

8-2

8-3

8-6

8-9

9-2

9-8

9-9 9-10 9-13 9-14 9-15 9-17 9-18 9-22 9-23

Introduction v

Chapter 10: Programming

Getting Started: Rolling a Die About TI-80 Programs

.......................

.............................

Creating and Executing Programs Editing Programs

PRGM CTL PRGM I/O

(Input/Output) Instructions

Calling Other Programs

.................................

(Control) Instructions

............................

...................

...............

10-2 10-4 10-5 10-6 10-7

10-11 10-14

Chapter 11: Applications

Chapter 12: Memory Management

Probability Experiments: Coins, Dice, and Spinners The Unit Circle and Trigonometric Curves Program: Newton’s Numerical Solve Routine Program: Numerical Integration

.....................

Program: Window Variables Store and Recall Graphing the Inverse of a Function Graphing a Piecewise Function Graphing Inequalities

..............................

Graphing a Polar Equation Program: Guess the Coefficients

Checking Available Memory Deleting Items from Memory Resetting the TI-80

................................

.....................

.........................

....................

........................

.......................

............

.........

..................

...

11-2 11-3 11-4 11-6 11-8

11-10 11-12 11-14 11-15 11-16

12-2 12-3 12-4

vi Introduction

Appendix A: Tables and Reference Information

Appendix B: Service and Warranty Information

Index

Table of TI-80 Functions and Instructions Menu Map TI-80 Variables

Battery Information Accuracy Information In Case of Difficulty Service and Support Information Warranty Information

........................................

...................................

...............................

.............................

...............................

...................

..............................

............

A-2 A-20 A-26

B-2

B-8 B-10 B-14 B-15

Introduction vii

Using this Guidebook Effectively

The structure of the TI-80 guidebook and the design of its pages can help you find the information you need quickly. Consistent presentation techniques are used throughout to make the guidebook easy to use.

Structure of the Guidebook

Page-Design Conventions

The guidebook is designed to teach you how to use the calculator.

Getting Started is a fast-paced, keystroke-by-keystroke introduction.

Chapter 1 describes general operation and lays the foundation for Chapters 2 through 10, which describe specific functional areas of the TI-80. Most chapters begin with a brief Getting Started introduction.

Chapter 11 contains application examples that incorporate features from different functional areas of the calculator. These examples can help you see how different functional areas work together to accomplish meaningful tasks.

Chapter 12 describes memory management.

When possible, units of information are presented on a single page or on two facing pages. Several page-design elements help you find information quickly.

Page headings—The descriptive heading at the top of the page or two-page unit identifies the subject of the unit.

General text—Just below the page heading, a short section of bold text provides general information about the subject covered in the unit.

Left-column subheadings—Each subheading identifies a specific topic or task related to the page or unit subject.

viii Introduction

InformationMapping Conventions

Specific text—The text to the right of a subheading presents detailed information about that specific topic or task. The information may be presented as paragraphs, numbered procedures, bulleted lists, or illustrations.

Page “footers”—The bottom of each page shows the chapter name, chapter number, and page number.

Several conventions are used to present information concisely and in an easily referenced format.

Numbered procedures—A procedure is a sequence of steps that performs a task. In this guidebook, each step is numbered in the order in which it is performed. No other text in the guidebook is numbered; therefore, when you see numbered text, you know you should perform the steps sequentially.

Lists with bullets—If several items have equal importance, or if you may choose one of several alternative actions, this guidebook precedes each item with a “bullet” (

Tables and charts—Sets of related information are presented in tables or charts for quick reference.

Keystroke examples—The Getting Started examples provide keystroke-by-keystroke instructions, as do the numerous short examples and several detailed examples that are identified with a

) to highlight it—like this list.



Introduction ix

Reference Aids

Several techniques have been used to help you look up specific information when you need it. These include:

A chapter table of contents on the first page of each chapter, as well as the full table of contents at the front of the guidebook.

A glossary at the end of this section, defining important terms used throughout the guidebook.

An alphabetical table of functions and instructions in Appendix A, showing their correct formats, how to access them, and page references for more information.

Information about system variables in Appendix A.

A table of error messages in Appendix B, showing the messages and their meanings and giving problem-handling information.

An alphabetical index at the back of the guidebook, listing tasks and topics you may need to look up.

x Introduction

Glossary

This glossary provides definitions for important terms that are used throughout this guidebook.

Argument

Command

Expression

Function

Home Screen

Instruction

List

Menu Items

An argument is an input upon which the value of a function depends.

A command is any entry submitted to the calculator using

. There are two types of TI-80 commands: instructions

and expressions.

An expression is a complete sequence of numbers, variables, functions, and their arguments that can be evaluated to a single answer. An expression returns the evaluated result to

ANS

A function, which may have arguments, returns a value and can be used in an expression.

A function is also the expression entered in the

editor used

in graphing.

The Home screen is the primary screen of the TI-80, where expressions can be entered and evaluated and instructions can be entered and executed.

An instruction, which may have arguments, initiates an action. Instructions are not valid in expressions. An instruction does not return a value to

ANS

A list is a set of values that the TI-80 can use for activities such as evaluating a function at multiple values and entering statistical data.

Menu items are shown on full-screen menus.

Introduction xi

Pixel

Real Number

Value

Variable

A pixel (picture element) is a square dot on the TI-80 display. The TI-80 display is 64 pixels wide and 48 pixels high.

On the TI-80, real numbers are individual decimal or fraction values.

A value is a single decimal or fraction number or a list of decimals or fractions.

A variable is the name given to a location in memory in which a value, an expression, a list, or another named item is stored.

xii Introduction



Getting Started: Do This First!

Getting Started contains two keystroke-by-keystroke examplesan interest rate problem and a volume problem operating and graphing features of the TI.80. You will learn to use the TI.80 more quickly by completing both of these examples first.

Contents

TI-80 Keyboard First Steps TI-80 Menus Entering a Calculation: Compound Interest Continuing a Calculation Defining a Function: Box with Lid Defining a Table of Values Zooming In on the Table Changing the Viewing Window Displaying and Tracing the Graph Zooming In on the Graph Other TI-80 Features

which introduce you to some principal

...................................

.......................................

......................................

...........

...........................

...................

..........................

...........................

......................

...................

...........................

..............................

2 3 4 5 6 7 8

9 11 12 13 14

Getting Started 1

TI-80 Keyboard

The keys on the TI.80 are grouped by color and physical layout to allow easy location of the key you need. The keys are divided into zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.

The Zones of the Keyboard

Graphing Keys

Editing Keys

Advanced Function Keys

Scientific Calculator Keys

Graphing Editing

Advanced Functions

Scientific Calculator

These keys are most frequently used to access the interactive graphing features of the TI-80.

These keys are most frequently used for editing expressions and values.

These keys are most frequently used to access the advanced functions of the TI-80.

These keys are most frequently used to access the capabilities of a standard scientific calculator.

& &

2 Getting Started

First Steps

Before beginning the two sample problems, follow the steps on this page to reset the TI-80 to its factory settings. (Resetting the TI-80 erases all previously entered data.) This ensures that following the keystrokes in this section produces the same actions.

1. Press ´ to turn the calculator on.

If the screen is very dark or blank, adjust the display contrast. Press and release 2, and then press and hold 8 (to make the display lighter) or press and hold 7 (to make the display darker). You can press

to clear the display.

2. Press and release 2, and then press µ. (Pressing

gives you access to the

printed at the upper left of the keys.

operation of the µ key.)

2nd

The

MEMORY

menu is displayed.

operations, which are

2nd

is the

MEM

3. Press 3 to select

The

4. Press 2 to select menu. The calculator is reset, and the

MEM CLEARED

RESET...

MEMORY RESET

RESET

message is displayed.

from the

MEMORY

menu is displayed.

from the

MEMORY RESET

menu.

Getting Started 3

TI-80 Menus

To leave the keyboard uncluttered, the TI.80 uses full-screen menus to display many additional operations. The use of specific menus is described in the appropriate chapters.

Displaying a Menu

When you press a key that displays a menu, such as

, that menu screen temporarily replaces the screen

where you are working.

fter you make a selection from a menu, you usually are

returned to the screen where you were.

Moving from One Menu to Another

menu key may display more than one menu name. The names appear on the top line. The name of current menu is highlighted, and the items in that menu are displayed. Use 9 or 6 to display a different menu.

Selecting an Item from a Menu

The number of the current item is highlighted. If there are more than seven items on the menu, a $ appears on the last line in place of the : (colon).

To select from a menu, you can either:

Use 8 and 7 to move the cursor to the item, and then press

Press the number of the item.

Note: The tenth item in a menu is number more than 10 items, they are numbered A, B, C, etc. To select one of these items, press letter.

Leaving without Making a Selection

To leave a menu without making a selection:

Press 2 . to return to the Home screen.

Press were.

Press the key for another screen or menu.

to return to the screen where you

. If there are

and then the

4 Getting Started

Entering a Calculation: Compound Interest

The TI.80 displays up to 8 16-characters lines so that you see an expression and its solution together. You can store values to variables, enter multiple instructions on one line, and recall previous entries.

Using trial and error, determine when an amount invested at 6% annual compounded interest will double in value.

1. For the first guess, compute the amount available at

the end of 10 years. Enter the expression just as you would write it. (Use 1000 for the amount.)

Press

1000

1.06

Z 10.

2. Press

to evaluate the expression.

The answer is shown on the right side of the display. The cursor is positioned on the next line, ready for you to enter the next expression.

3. The next guess should be greater than 10 years. Make

the next guess 12 years. To calculate the amount after 12 years, press

1000

1.06

, followed by

Getting Started 5

Continuing a Calculation

To save keystrokes, you can use the Last Entry feature to recall the last expression entered and then edit it for a new calculation. In addition, the next expression can be continued from the previous result.

1. The next guess should be less than, but close to, 12

years. Compute the amount available at the end of

11.9 years, using the Last Entry feature. Press 2, followed by

(the second function of

The last calculated expression is shown on the next line of the display. The cursor is positioned at the end of the expression.

2. You can edit the expression. Press 6 to move the

cursor over the

Press

. Then type

to change 12 to

1.9

to evaluate the expression.

Note: This process can be continued to obtain a solution with the desired accuracy.

3. You can continue a calculation using the result of the

last calculation. For example, if the final amount determined above is to be divided among seven people, how much would each person get?

To divide the last calculation by seven, press e followed by

As soon as you press e, beginning of the new expression.

is displayed at the

ANS

that contains the last calculated result. In this case,

contains 2000.505716.

ANS

11.9

is a variable

6 Getting Started

Defining a Function: Box with Lid

Take an 8½"×11" sheet of paper and cut X by X squares from two corners and X by (X+B) rectangles from the other two corners. Now fold the paper into a box with lid. What X would give the maximum volume V of a box made in this way? Use tables and graphs to determine the solution.

Begin by defining a function that describes the volume of the box.

From the diagram: 2X + A = W

2X + 2B = L V = A B X

Substituting: V = (W – 2X) (L à 2 – X) X

If necessary, press z †

MODE

. Then press y .

FLOAT

to change the

‘

return to the Home screen and clear it.

1. Press

¿ ƒ

8.5

to store the width of

the paper.

Press

¿ ƒ

to store the length of

the paper.

2. You define functions for tables and graphs on the

edit screen.

Press o to access this screen.

3. Enter the function for volume as Y1. Press £

¹ 2 @ ¤ £

to define function enter

quickly without pressing

L ¥ 2 ¹ @ ¤ @

in terms of X. (@ lets you

ƒ Í

The = sign is highlighted to show that Y1 is selected.

XABXB

Getting Started 7

Defining a Table of Values

The table feature of the TI.80 provides numeric information about a function. Use a table of values from the previously defined function to estimate an answer to the problem.

screen.

to accept

to define the table increment

(above

1. Press y

TABLE SETUP

2. Press

3. Press .5

4. Press y

Note that the maximum value is around

and 2.

(above

TBLMIN=0

) to display the

) to display the table.

, between

1.5

TBL=.5

5. Press and hold † to scroll the table until the sign

change appears. Note that the maximum length of for this problem occurs where the sign of

(volume) becomes negative.

6. Press y

. Note that

TBLMIN

has changed to

reflect the first line of the table you last displayed.

8 Getting Started

Zooming In on the Table

You can adjust the way a table is displayed to get more detailed information about any defined function. By varying the value of @TBL, you can “zoom in” on the table.

1. Adjust the table setup to get a more accurate

estimate of the maximum size of the cutout. Press

to set

TBLMIN

. Press .1 to set

Tbl

2. Press y

3. Use † and } to scroll the table. Note that the

maximum value displayed is

. The maximum occurs at

X=1.6

, which occurs at

33.072

1.5<X<1.7

Getting Started 9

4. Press y

Press

.01

. Press

to set

1.5

TBL

to set

TBLMIN

5. Press y

Two “equal” maximum values are shown,

X=1.58

6. Press † or } to move the cursor to

move the cursor into the of the display shows the value of precision,

and

33.073824

and use † and } to scroll the table.

33.074

X=1.59

. Press ~ to

1.58

column. The bottom line

1.58

in full

7. Press † to display the “other” maximum. The value

in full precision is

1.59

33.073908

. This would be the maximum volume of the box if you could cut your piece of paper at .01-inch increments.

10 Getting Started

Changing the Viewing Window

The viewing window defines the portion of the coordinate plane that appears in the display. The values of the Window variables determine the size of the viewing window. You can view and change these values.

1. Press

to display the Window variables edit screen. You can view and edit the values of the Window variables here.

The standard Window variables define the viewing window as shown.

XMIN, XMAX, YMIN

define the boundaries of the display.

, and

XSCL

YMAX

and

define the distance between tick marks on the X and

axes.

2. Press 0

to define

XMIN

3. You can enter expressions to define values in the window editor. Press

8.5

4. Press

5. Press 0

stored in

. The expression is evaluated, and

XMAX

. Press

to accept

to define the

XSCL

4.25

as 1.

Window variables.

YSCL

XMIN

YMAX

XSCL

XMAX

YSCL

YMIN

Getting Started 11

Displaying and Tracing the Graph

Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function with TRACE.

1. Press

to graph the selected function in the

viewing window.

The graph of

Y1=(W–2X)(Là2–X)X

is shown in the

display.

2. Press ~ once to display the free-moving cursor just to the right of the center of the screen. The bottom line of the display shows the X- and Y-coordinate values for the position of the graph cursor.

3. Use |, ~, }, and † to position the free-moving cursor at the apparent maximum of the function.

As you move the cursor, X- and Y-coordinate values are updated continually to reflect the cursor position.

4. Press

. The Trace cursor appears on the

function. 1 in the upper right corner of the display shows that the cursor is on

, you trace along

at each X.

, one X dot at a time, evaluating

. As you press | and

5. Press | and ~ until you are on the maximum Y value. This is the maximum of

for the X pixels.

Y1(X)

(There may be a maximum value “in between” pixels.)

12 Getting Started

Zooming In on the Graph

You can magnify the viewing window around a specific location using the Zoom instructions to help identify maximums, minimums, roots, and intersections of functions.

1. Press

to display the

ZOOM

menu.

This menu is typical of TI-80 menus. To select an item, you may either press the number to the left of the item, or you may press † until the item number is highlighted and then press

2. To

ZOOM IN

, press 2. The graph is displayed again.

The cursor has changed to indicate that you are using a Zoom instruction.

3. Use |, }, ~, and † to position the cursor near the maximum value on the function, and press

The new viewing window is displayed. It has been adjusted in both the

and Y directions by factors of

4, the values for Zoom factors.

4. Press

to display the new window variable

values.

Getting Started 13

Other TI.80 Features

Getting Started has introduced you to basic calculator operation and the table and function graphing features of the TI-80. The remainder of this Guidebook describes these features in more detail and also covers other capabilities of the TI-80.

Fractions

Graphing

Tables

Lists

Statistics

Programming

You can enter fractions directly from the keyboard and perform calculations with fractions. You can convert between fractions and their decimal equivalents. In

MANSIMP

mode, you can simplify fractions step-by-step. The TI-80 tells you when a fraction can be simplified and shows the common factor after simplification (Chapter 3).

You can store, graph, and analyze up to four functions (Chapter 4) and up to three parametric functions (Chapter 5). You can use Draw operations to annotate graphs (Chapter 7).

You can create function evaluation tables to analyze multiple functions simultaneously (Chapter 6).

You can enter and save up to six lists for use in statistical analysis. You also can use lists to evaluate expressions at multiple values simultaneously (Chapter 8).

You can perform one-variable and two-variable list-based statistical analysis, including regression analysis, and plot the data as histograms, points, x-y lines, or box-and-whisker plots. You can define and save three statistical plot definitions (Chapter 9).

You can enter and save programs that include extensive control and input/output instructions (Chapter 10)

14 Getting Started

Chapter 1: Operating the TI-80

This chapter describes the TI.80 and provides general information about its operation.

Chapter Contents

Turning the TI.80 On and Off Setting the Display Contrast The Display

......................................

.......................

........................

Entering Expressions and Instructions The Edit Keys Setting Modes TI.80 Modes Variable Names

....................................

......................................

...................................

Storing and Recalling Variable Values Last Entry Last Answer TI.80 Menus The EOS (Equation Operating System) Error Conditions

........................................

......................................

VARS

and

Y.VARS

..................................

......................

Menus

..................

...............

................

1-2 1-3 1-4 1-6 1-8

1-9 1-10 1-12 1-13 1-14 1-16 1-17 1-19 1-20 1-22

Operating the TI-80 1-1

Turning the TI-80 On and Off

To turn the TI.80 on, press the ´ key. To turn it off, press and release y, and then press ®. After about five minutes without any activity, the APD™ (Automatic Power Down™) feature turns the TI.80 off automatically.

Turning the Calculator On

Turning the Calculator Off

APD™ (Automatic Power Down™)

Batteries

Press ´ to turn the TI-80 on.

If you pressed y ® to turn the calculator off, the display shows the Home screen as it was when you last used it, and errors are cleared.

If APD turned the calculator off, the display returns to the same screen or editor in which you left it. See “APD (Automatic Power Down)” below.

Press and release 2, and then press ® to turn the TI-80 off.

Any error condition is cleared.

All settings and memory contents are retained by the Constant Memory

feature.

To prolong the life of the batteries, APD turns the TI-80 off automatically after several minutes without any activity. When you press ´, the calculator shows the same screen or editor in which you left it.

If an error message was displayed when APD turned the TI-80 off, the error is cleared, and the display returns to a blank line on the Home screen.

If a menu was displayed, the display returns to the screen or editor from which you called the menu.

All settings and memory contents are retained by the Constant Memory feature.

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

The TI-80 uses two CR2032 lithium batteries. To replace the batteries without losing any information stored in memory, follow the directions in Appendix B.

1-2 Operating the TI-80

Setting the Display Contrast

The brightness and contrast of the display depend on room lighting, battery freshness, viewing angle, and the adjustment of the display contrast. The contrast setting is retained in memory when the TI.80 is turned off.

Adjusting the Display Contrast

When to Replace Batteries

You can adjust the display contrast to suit your viewing angle and lighting conditions. As you adjust the contrast setting, the display becomes lighter or darker. A highlighted number in the upper right corner changes to indicate the current contrast setting; 0 is the lightest, and 9 is the darkest.

To adjust the display contrast:

1. Press and release the 2 key.

2. Use one of two keys:

To increase the contrast (darken the screen), press and hold 7.

To decrease the contrast (lighten the screen), press and hold 8.

Note: The display may become completely blank if you adjust the contrast setting too low. If this happens, press and release

, and then press and hold 7 until the display reappears.

As you use the TI-80, the battery voltage will gradually drop, and the display will dim. You can adjust the contrast to darken the display when this happens. If the display is dim and adjusting the contrast to level 9 does not make it dark enough, you should replace the batteries. Refer to Appendix B for instructions on how to change the batteries.

Note: After you change batteries, the display contrast may appear very dark. Press and release y, and then press and hold 8 to lighten the display.

Operating the TI-80 1-3



The Display

The TI.80 displays both text and graphs. Graphs are described in Chapters 4 and 5.

Home Screen

Displaying Entries and Answers

Returning to the Home Screen

The primary screen of the TI-80 is the Home screen. You enter instructions to be executed, expressions to be evaluated, and see the results on the Home screen.

When text is displayed, the TI-80 screen can show a maximum of eight lines with 16 characters each.

If all lines of the display are filled, text “scrolls” off the top of the display.

If an expression on the Home screen, the Y= editor (Chapter 4), or the program editor (Chapter 10) is longer than one line, it wraps to the beginning of the next line.

On numeric editors such as the Window screen (Chapter 4), an expression scrolls to the left and right.

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

Entry Answer

The mode settings (pages 1-9 through 1-11) control the way the calculator interprets expressions and displays answers.

If an answer is too long to display in its entirety, you can press

and 6 to scroll the answer so that you can view all of it. In the second example below, the open brace without a corresponding close brace indicates that the list is too long to be displayed in its entirety.

Entry Answer

Answer

Answer (scrolled)

To return to the Home screen from any other screen, press

y .

1-4 Operating the TI-80

Display Cursors

Busy Indicator

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

Cursor Appearance Meaning

Entry Blinking

(insert) Blinking

INS

2nd

ALPHA

memory “full” Checkerboard

Graphs and the screens for viewing and editing tables and lists have different cursors, which are described in the appropriate chapters.

When the TI-80 is calculating or graphing, a vertical line shows in the upper right of the display as a busy indicator. During a pause in a program, the busy indicator is a dotted line.

Blinking

rectangle





The next keystroke is entered at the cursor; it types over any character.

The next keystroke is inserted at the cursor.

The next keystroke is a operation.

The next keystroke is an alphabetic character.

You have entered the maximum number of characters in a name, or memory is full.

2nd

Operating the TI-80 1-5

Entering Expressions and Instructions

In most places where a value is required, you can use an expression to enter the value. You can enter instructions, which initiate an action, on the Home screen or in the program editor (Chapter 10).

Expressions

Entering an Expression

An expression is a complete sequence of numbers, variables, functions, and their arguments that evaluate to a single

L O G

is an expression. On the TI-80, you

, regardless of the cursor

) rules, and then the

4 5

. (If you type

, the TI-80 interprets

LOG

answer. For example, enter an expression in the same order as you would write it.

You can create expressions 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.

To create an expression, you enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press location. The entire expression is evaluated according to Equation Operating System (EOS answer is displayed.

Note: EOS rules determine the order in which operations are completed (page 1-20).

Most TI-80 functions and operations are symbols with several characters in them. You must enter the symbol from the keyboard or menu. You cannot spell it out. For example, to calculate the log of 45, you must press l type in the letters the entry as implied multiplication of the variables

Calculate 3.76 ÷ (-7.9 + ‡5) + 2 log45.



3.76

e c ·

]

d « 2 l

7.9

. You cannot

, and G.)

L, O

Multiple Entries on a Line

1-6 Operating the TI-80

To enter more than one expression or instruction on a line, separate them with a colon (:). They are all stored together in Last Entry (page 1-15).

Entering a Number in Scientific Notation

Functions

Instructions

Interrupting a Calculation

To enter a number in scientific notation:

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

This value can be an expression.

2. Press 2 ^.

is displayed.

3. If the exponent is negative, press ·, and then type the

exponent, which can be one or two digits.

Entering a number in scientific notation does not cause the answers to be displayed in scientific notation. The display format is determined by the mode settings (pages 1-9 through 1-11) and the size of the number.

A function returns a value. For example,

, ×, −, +, ‡, and

LOG

are functions. Some functions take more than one argument, which is indicated by a two arguments in this example:

at the end of the name.

(

MIN(5,8)

An instruction initiates an action. For example,

requires

MIN(

CLRDRAW

is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. Some instructions take more than one argument, which is indicated by a end of the name. example:

LINE(1,1,3,3)

requires four arguments in this

LINE(

at the

(

While the busy indicator is displayed, indicating that a calculation or a graph is in progress, you can press ´ to stop the calculation. (There may be a delay.)

Operating the TI-80 1-7

The Edit Keys

The arrow keys near the upper right of the keyboard control the movement of the cursor. In normal entry, a keystroke types over the character or characters at the position of the cursor. The 4 and y / keys delete or insert characters.

Key(s) Action(s)

2 6

2 9

Moves the cursor within an expression. These keys repeat when you hold them down.

Moves the cursor between lines within an expression. These keys repeat when you hold them down.

On the top line of an expression on the Home screen, moves the cursor to the beginning of the expression.

On the bottom line of an expression on the Home screen,

moves the cursor to the end of the expression.

Moves the cursor to the beginning of an expression.

Moves the cursor to the end of an expression.

Evaluates an expression or executes an instruction.

On a line with text on the Home screen, clears (blanks) the current line.

On a blank line on the Home screen, clears everything on the Home screen.

In an editor, clears (blanks) the expression or value where the cursor is located; it does not store a zero.

Deletes the character at the cursor. This key repeats.

Lets you insert characters at the underline cursor. To end insertion, press y / or a cursor key.

Next key press is a

operation (the gold-colored label

2nd

printed to the left above a key). The cursor changes to . To cancel

Next key press is an

, press y again.

2nd

character (the light gray

ALPHA

character to the right above a key). The cursor changes to To cancel

Sets

ALPHA ALPHA-LOCK

ALPHA

ALPHA-LOCK

character. The cursor changes to . To cancel

, press

Allows you to enter an mode without pressing

, press

or a cursor key.

; each subsequent key press results in an

mode or a T in

FUNC

first.

PARAM

1-8 Operating the TI-80

Setting Modes

Modes control how numbers and graphs are displayed and interpreted by the calculator. Mode settings are retained by the Constant Memory feature when the TI.80 is turned off.

Checking MODE Settings

Changing MODE Settings

Leaving the MODE Screen

Setting a Mode from a Program

Press 3 to display the

screen. The current settings

MODE

are highlighted. The settings are described on the following pages.

NORMAL SCI FLOAT 0123456789 RADIAN DEGREE aÀbºc bºc AUTOSIMP MANSIMP FUNC PARAM CONNECTED DOT SEQUENTIAL SIMUL

Numeric display format. Number of decimal places. Unit of angle measure. Type of fraction display. Whether to simplify fractions. Type of graphing. Whether to connect graph points. Whether to plot simultaneously.

To change the mode setting:

1. Press 8 or 7 to move the cursor to the line of the setting

that you want to change. The setting that the cursor is on blinks.

2. Press 9 or 6 to move the cursor to the setting that you

want.

3. Press

To leave the

screen:

MODE

Press the appropriate keys to go to another screen.

Press y . or

to return to the Home screen.

You can set a mode from a program by entering the name of the mode as an instruction; for example,

FUNC

FLOAT

From a blank line in the program editor (Chapter 10), press

to display a menu of the mode names, and then select

the name. The name is copied to the cursor location.

Operating the TI-80 1-9

TI-80 Modes

The TI.80 has eight mode settings. They control how numeric entries are interpreted, how answers are calculated or displayed, and how graphs appear in the display. Modes are set on the MODE screen (page 1.9).

NORMAL SCI

FLOAT Fixed Decimal

Notation formats affect only how an answer is displayed on the Home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format.

NORMAL

display format is the way in which we usually express decimal numbers, with digits to the left and right of the decimal, as in

(scientific) notation expresses numbers in two parts. The

SCI

12345.67

significant digits can be displayed with one digit to the left of the decimal. The appropriate power of 10 displays to the right

, as in

1.234567í4

Note: If you select normal display format, but the answer cannot be displayed in 10 digits or the absolute value is less than .001, the TI-80 displays the answer in scientific notation.

Decimal settings affect only how an answer is displayed on the Home screen. You can enter a number in any format. The decimal settings apply to both notation formats.

(floating) decimal setting displays up to 10 digits, plus

FLOAT

the sign and decimal.

The fixed decimal setting lets you select the number of digits (

to 9) to be displayed to the right of the decimal. The

displayed value is rounded based on the number of digits you selected. The actual value is stored and used in calculations. Place the cursor on the number of decimal digits you want, and press

Note: In the program editor, the format for fixed decimal settings is

n. Enter n as an integer from 0 to 9. The mode

FIX

is changed to fixed decimal when the program is executed.

1-10 Operating the TI-80

RADIAN DEGREE

aÀbºc bºc

AUTOSIMP MANSIMP

FUNC PARAM

CONNECTED DOT

SEQUENTIAL SIMUL

The angle mode controls:

How the calculator interprets angle arguments in

COS, TAN

How the calculator returns angle answers to

TAN

RADIAN

, and polar-to-rectangular conversions.

, and rectangular-to-polar conversions.

mode interprets angle arguments as radians and

SIN

COS

returns angle answers in radians.

DEGREE

mode interprets angle arguments as degrees and

returns angle answers in degrees.

displays fraction results as mixed numbers; for

aÀbºc

example, the result of

displays fraction results as simple fractions; for example,

bºc

the result of

AUTOSIMP

1º3 + 4º3

automatically simplifies fraction results to their

1º3 + 4º3

is displayed as

5º3

1À2º3

lowest terms before displaying them; for example, the result of

2º6 + 2º6

MANSIMP

simplification; for example, the result of displayed as

FUNC

expressed in terms of

PARAM

is displayed as

2º3

displays fraction results without automatic

4º6

2º6 + 2º6

(function) graphing plots functions where Y is

(Chapter 4).

(parametric) graphing plots relations where X and

are each expressed in terms of T (Chapter 5).

CONNECTED

draws line segments between the calculated

points of the selected functions.

plots only the calculated points of the selected functions.

DOT SEQUENTIAL

graphing evaluates and plots one function

completely before the next function is evaluated and plotted.

(simultaneous) graphing evaluates and plots all

SIMUL

selected functions for a single value of Parametric mode, evaluated and plotted a

and Y are selected pairs. They are

value at a time.

, one at a time. In

Operating the TI-80 1-11

Variable Names

On the TI.80 you can enter, name, and use several types of data: numeric values (including fractions), lists, functions, and statistical plots.

Variables and Defined Items

The TI-80 uses both user-assigned and pre-assigned names for variables and other items saved in memory.

Variable Type Names

Numeric values

, ..., Z, q (single character only).

A, B

(including fractions)

Lists

L1, L2, L3, L4, L5, L6

(on the

keyboard).

Functions

Parametric equations

Statistical plots

System variables

Y1, Y2, Y3, Y4 FUNC

X1î/Y1

editor in

PLOT1, PLOT2, PLOT3 STAT PLOTS

XMIN, XMAX

(on the Y= editor in

mode).

X2î/Y2 PARAM

X3î/Y3

mode).

menu).

, and others (on various

(on the

menus).

Programs have user-defined names also and share memory with variables. Program names can be up to seven characters long. Programs are entered and edited from the program editor (Chapter 10).

You can store to lists (Chapter 8), system variables such as

XMAX

(Chapter 4) or

TBLMIN

(Chapter 6), and all

functions (Chapters 4 and 5) from the Home screen or from a program. You can store to lists (Chapters 8 and 9) and functions (Chapters 4 and 5) from editors. You can also store to a list element (Chapter 8).

For more information about system variables, see Appendix A.

1-12 Operating the TI-80

Storing and Recalling Variable Values

Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used.

Storing Values in a Variable

Displaying a Variable Value

Using a Variable in an Expression

You can store a value to a variable from the Home screen or a program using the § key. Begin on a blank line.

1. Enter the value that you want to store (this can be an

expression).

2. Press §. The symbol ! is copied to the cursor location.

3. Press

and then the single letter of the variable to

which you want to store the value.

4. Press

. If you entered an expression, it is evaluated.

The value is stored in the variable.

To display the value of a variable, enter the variable name on a blank line on the Home screen, and then press

. You can

enter the name of the variable in one of the following ways:

Press

and the letter of the variable (for user-defined

variables).

Press 2 and the name of the list.

Press

and select the type and name of the variable

(for system variables).

Press 2

and select the type and name of the

function.

To use the current value of a variable in an expression, just enter the variable name in the expression.

Operating the TI-80 1-13

Last Entry

When you press an instruction, the expression or instruction is stored in an area called Last Entry, which you can recall. When you turn the TI.80 off, Last Entry is retained in memory.

Using Last Entry

Displaying a Previous Entry

on the Home screen to evaluate an expression or execute

You can recall Last Entry and edit it from the Home screen.

. The current line is cleared, and the Last

, you can recall the previous

. Last Entry displays previous

A B C

Press y Entry is copied to the line. The cursor is positioned at the end of the entry. Because the TI-80 updates the Last Entry storage area only when you press entry even if you have begun entering the next expression. However, when you recall Last Entry, it replaces what you have typed.



The TI-80 keeps previous entries (up to a total of 80 bytes) in Last Entry. You can display and edit those entries by continuing to press 2 entries in a loop, beginning with newest entry and moving to the oldest entry. Once the oldest item is displayed, 2 displays the newest item again.



§ ?

When you press y the item on the current line.

1-14 Operating the TI-80

again, the previous item replaces

Re.executing the Previous Entry



on a blank line on the

To execute Last Entry, press Home screen. The entry is executed, but it does not display again.

¸ ? ¸ ¸ ¸

« 1

§ ?

Multiple Entries on a Line



To enter more than one expression or instruction on a line, separate them with a colon ( Last Entry.

If the previous entry contained more than one expression or instruction, separated with a colon (page 1-6), they all are recalled. You can recall all entries on a line, edit any of them, and then execute all of them.

Using the equation A=pr of a circle that covers 200 square centimeters. Use 8 as your first guess.

Now try this.

y 6

Continue until the answer is as accurate as you want.

y /

R y

.95

). They are all stored together in

, use trial and error to find the radius

Operating the TI-80 1-15

Last Answer

When an expression is evaluated successfully from the Home screen or from a program, the TI.80 stores the answer to a variable, ANS (Last Answer). ANS may be a decimal number, a fraction, or a list. When you turn the TI.80 off, the value in ANS is retained in memory.

Using Last Answer (ANS) in an Expression



Continuing an Expression



Storing Answers



You can use the variable most places. When you press y ±, the variable name is copied to the cursor location. When the expression is evaluated, the TI-80 uses the value of

Calculate the area of a garden plot that is 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.

1.7

4.2

147

You can use the value in expression without entering the value again or pressing

The TI-80 “types” the variable name function.

¸ p

9.9

To store an answer, store evaluate another expression.

Calculate the area of a circle of radius 5 meters. Then calculate the volume of a cylinder of radius 5 meters and height 3.3 meters. Store the result in the variable

e y

. On a blank line on the Home screen, enter the function.

to represent the last answer in

ANS

in the calculation.

ANS

as the first entry in the next

ANS

followed by the

ANS

to a variable before you

ANS

¸ p

3.3

§ ? ¸

1-16 Operating the TI-80

TI-80 Menus

To leave the keyboard uncluttered, the TI.80 uses full.screen menus to give you access to many additional operations. The use of specific menus is described in the appropriate chapters.

Moving from One Menu to Another

Selecting an Item from a Menu



Some menu keys, such as The names of the menus appear on the top line. The current menu is highlighted and the items in that menu are displayed.

Press 9 or 6 to move the cursor to a different menu.

The number of the current item is highlighted. If there are more than seven items on the menu, a $ appears on the last line in place of the name. Menu items, such as (ellipsis marks) display another menu.

There are two methods of selecting from a menu.

Press the number of the item you want to select.

Press 8 and 7 to move the cursor to the item you want to select, and then press

‡

27 .

to display the

‡

, you may either press 4 or press 8 8

and then press

Calculate

1. Press

2. To select

3. Enter

, display more than one menu.

(colon) between the menu number and

VARS WINDOW

MATH

to evaluate the expression.

, that end in ...

menu.

Operating the TI-80 1-17

Leaving a Menu without Making a Selection

There are several ways to leave a menu without making a selection from the menu.

To return to the Home screen, press 2 ..

To return to the screen where you were, press

To display a different menu, press the appropriate key, such as

To select another screen, press the appropriate key, such as

)

1-18 Operating the TI-80

The VARS and Y.VARS Menus

You may want to use the names of system variables (such as XMIN) and functions (such as Y1) in an expression. You may also want to store values directly to those variables. Use the VARS or Y.VARS menus to access the names.

VARS Menu

Y.VARS Menu

Copying a Name from a VARS or Y.VARS Menu

The as table variables such as

Press

menu displays the names of window variables such

VARS

XMIN

and

to display the

, statistics variables such as v and

TSTEP

TBLMIN

menu. Some of the items

VARS

, and

display more than one menu of variable names.

VARS 1: WINDOW... 2: STATISTICS... 3: TABLE... 4: SIMPFACTOR...

The

Y.VARS

menus display the names of functions and the

Names of

, EQ, and

X/Y TBLMIN

Factor last used by

and T variables.

X, Y

BOX

and

TBL

variables.

function.

SIMP

instructions to select or deselect functions from a program or the Home screen.

Press 2

to display the

Y.VARS

menu. Then press

or 6 to select the type of variable you want.

Y XTàYT ONàOFF

To copy a variable name from a

1. Press

Displays a menu of names of Yn functions. Displays a menu of names of XnTàYnT equations. Lets you select/deselect functions.

or 2

VARS

. The

VARS

Y.VARS

menu:

Y.VARS

menu is

displayed.

2. Select the type of variable you want.

3. Press

to select the name you want from the menu. It

is copied to the cursor location.

Operating the TI-80 1-19



EOS (Equation Operating System)

The Equation Operating System (EOS™) defines the order of operations for the calculator expressions. EOS lets you enter numbers and functions in a simple, straightforward sequence.

Order of Evaluation

that is, the order in which the TI.80 evaluates functions in

A function returns a value. EOS evaluates the functions in an expression in the following order.

Functions that are entered after the argument, such as

Powers and roots, such as

Implied multiplication where the second argument is a

22!, 45

, and

SIMP

2^5

‡

number, variable name, or list, or begins with an open parenthesis, such as

Single-argument functions that precede the argument,

such as

Implied multiplication where the second argument is a

‡

4A, (A+B)4,

, or

SIN B

LOG 3

4(A+B)

multi-argument function or a single-argument function that precedes the argument, such as

ASIN 2

Permutations (

Multiplication and division (including

Addition and subtraction.

Test functions, such as > or .

Conversion functions:

) and combinations (

nPr

FRAC

2NDERIV(Añ,A,6)

INT÷

DEC

nCr

aÀbºc

, and

bºc

1-20 Operating the TI-80

Within a priority group,

EOS evaluates functions from left to right. However, two or more single-argument functions that precede the same argument are evaluated from right to left. For example,

SIN(FPART(LN 8))

SIN FPART LN 8

is evaluated as

Calculations within a pair of parentheses are evaluated first. Multi-argument functions, such as

NDERIV(Añ,A,6)

, are

evaluated as they are encountered.

The conversion functions

FRAC

DEC

aÀbºc

, and

bºc

can be used only at the end of a command line with one exception: they can be followed by a store instruction.

Implied Multiplication

Parentheses

Negation

The TI-80 recognizes implied multiplication. For example, it understands

4SIN 45, 5(1+2)

, and

(2×5)7

as implied

multiplication.

All calculations inside a pair of parentheses are completed first. For example, in the expression evaluates the portion inside the parentheses, multiplies the answer,

, by 4.

4(1+2)

, EOS first

, and then

1+2

You can omit any right (closing) parenthesis at the end of an expression. All “open” parenthetical elements are closed automatically at the end of an expression and preceding the (store) or display-conversion instructions.

Note: Parentheses are also used to enclose the arguments for certain functions, for example,

NDERIV(Añ,A,6)

. In these

cases, parentheses do not indicate implied multiplication.

To enter a negative number, use the negation function. Press

, and then enter the number. On the TI-80, negation is in the fourth group in the EOS hierarchy. Functions in the first group, such as squaring, are evaluated before negation.

For example, parentheses to square a negative number:

is a negative number (or 0);

(L9)

. Use

Note: Use the | key for subtraction and the · key for negation. If you press | to enter a negative number, as in

, or if you press · to indicate subtraction, as in

is an error. If you press

as implied multiplication (

A QLB

B, it is interpreted

9 · 7

Operating the TI-80 1-21

, it

Error Conditions

The TI.80 detects any errors at the time it evaluates an expression, executes an instruction, plots a graph, or stores a value. Calculations stop and an error message with a menu is displayed immediately. Error codes and conditions are described in detail in Appendix B.

Diagnosing an Error

Correcting an Error

If the TI-80 detects an error, it displays the error screen.

The top line indicates the general type of error, such as

SYNTAX

DOMAIN

. For additional information about each

error message, see Appendix B.

If you select

, the cursor is displayed at the location

GOTO

where the error was detected.

Note: If a syntax error was detected in the contents of a

function during program execution,

user to the

If you select

editor, not to the program.

or press y . or

QUIT

GOTO

returns the

, you return

to the Home screen.

To correct an error:

1. Note the type of the error.

2. Select

, if that option is available; and look at the

GOTO

expression for syntax errors, especially at and before the cursor location.

3. If the error in the expression is not readily apparent, turn

to Appendix B, and read the information about the error message.

4. Correct the expression.

1-22 Operating the TI-80

Chapter 2: Math, Angle, and Test Operations

This chapter describes the math, angle, and relational operations that are available on the TI.80. The most commonly used functions are accessed from the keyboard; others are accessed through menus.

Chapter Contents

Getting Started: Lottery Chances Using the TI-80 Functions Keyboard Math Operations

MATH MATH MATH NUM MATH PRB ANGLE TEST

Operations

(Number) Operations

(Probability) Operations

Operations

(Relational) Operations

..........................

.........................

...........................

................................

.......................

....................

...................

.................

2-2 2-3 2-4

2-7 2-10 2-12 2-14 2-16

Math, Angle, and Test Operations 2-1

Getting Started: Lottery Chances

Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to enter a lottery where six numbers will be drawn out of 50.

To win, you must pick all six numbers (in any order). What is the probability of winning if you buy one ticket? What is the probability of winning if you buy five tickets?

1. Determine the number of combinations possible. On the Home screen, press items. Press Press 3 to select

nCr

items selected.

to enter the total number of

to display the

MATH PRB

. Press 6 to enter the number of

2. Press

to evaluate the expression. This is the total number of possible combinations of 6 numbers drawn from a set of 50 numbers. With one ticket, you have one chance in 15,890,700 of winning.

3. To calculate the probability of winning with one ticket, press

e 2 ±

. The answer is too large to display in fixed notation; therefore, it is shown in scientific notation. 0.00000006292988981 is the decimal equivalent.

4. To calculate the probability of winning with five tickets, press p

. Again, the answer is too

small to display in fixed notation. The decimal equivalent is 0.000000314649449.

2-2 Math, Angle, and Test Operations

Using the TI-80 Functions

This page contains some general information you should know about the TI.80 functions described in Chapter 1.

Using Lists with Functions

Using Fractions with Functions

Functions that are valid for lists return a list calculated on an element-by-element basis. If two lists are used in the same expression, they must be the same length. For more information about lists, see Chapter 8.

Some math functions (+, –, ×, à,

ñ, úbº

úaÀbº

DEC

)

accept fractions as input values. All other functions convert fractions to decimals before operating on them. For more information about fractions, see Chapter 3.

Math, Angle, and Test Operations 2-3

Keyboard Math Operations

The most commonly used math functions are on the keyboard. The keyboard math operations can be used with decimal numbers, fractions (except as noted), expressions, and lists.

+ (Add) – (Subtract)

(Multiply)

(Divide)

Trig Functions

The basic arithmetic functions are: addition «, subtraction |, multiplication p, and division e. Each argument for these functions can be a list.

valueA valueA

valueB, valueAìvalueB

valueB, valueAàvalueB

The trigonometric functions are interpreted according to the current

RADIAN/DEGREE

mode setting. (Refer to page 1-9 for

instructions on changing the mode setting.) For example,

SIN 30

RADIAN

mode returns

.9880316241

; in

DEGREE

mode, it returns .5. Each argument for the trigonometric functions may be a list.

SIN SIN

value

COS

, and

value

TAN

value

TAN

are the inverse trig functions (arcsine,

arccosine, and arctangent).

value

SIN RADIAN Mode

COS

value

TAN

value

(inverse, V) may be used with numbers, expressions, or

(Inverse)

lists. The multiplicative inverse is the equivalent of the reciprocal, 1

value

2-4 Math, Angle, and Test Operations

(Power)

(Square)

‡

(Square Root)

(power, Z), 2 (square, a), and ‡ (square root, 2 ]) may

be used with decimal numbers, fractions, expressions, or lists. When used with a fraction,

power, value

value

‡

returns a decimal number.

value

‡

Note: Raising a negative number to a noninteger power can result in a complex number, which returns an error.

LOG 10^ LN

These functions find the logarithm l, power of ten 2 h, and natural log x of the specified value or list of values.

value

LOG

( 2 s) returns the constant e raised to a power or list of

powers.

power

10^

returns the value of the constant e.

e^1

value

Math, Angle, and Test Operations 2-5

(Negation)

(negation, ·) returns the negative of a number, expression,

or list. The narrow negation symbol ( from the subtraction or minus (

value

EOS rules (Chapter 1) determine when negation is evaluated. For example, is evaluated before negation. Use parentheses to square a negated number,

returns a negative number because squaring

(LA)

) distinguishes negation

–

ABS

(Pi)

(absolute value, 2 P) returns the absolute value of a

ABS

number, expression, or list.

value

ABS

Pi (2 T) is stored as a constant in the TI-80. Press 2

to copy the symbol

3.141592654

is displayed for p, but 3.1415926535898 is used

to the cursor location. The number

internally in calculations.

2-6 Math, Angle, and Test Operations

MATH MATH Operations

To display the MATH MATH menu, press I. When you select a menu item, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.

MATH MATH Menu

INT÷

MATH NUM PRB 1:

INT÷

DEC

‡

6: NDERIV(

On the Home screen or from a program,

MATH MATH

Displays quotient and remainder. Displays answer in decimal form. Cube. Cube root.

root.

Numerical derivative.

(integer divide,

INT÷

, item 1) returns the quotient (or quotient and remainder) resulting from the division of two integers. Each argument can be a list.

integerA

When symbols

Note: If

integerB

INT÷

is executed on the Home screen, it displays the

INT÷

for the quotient and R= for the remainder.

is embedded in an expression, Q= and R= may

INT÷

not be displayed.

When used with lists,

If the result of

INT÷

returns a list of quotients only.

INT÷

is used in subsequent calculations, the

remainder is dropped, and only the quotient is used.

The quotient from

is returned to

INT÷

ANS

Math, Angle, and Test Operations 2-7

DEC

(convert to decimal,

DEC

answer in decimal form. and at the end of an

value8

DEC

expression8

expression. value

DEC

MATH MATH

can only be used after a

DEC

, item 2) displays an

can be a list.

value

(Cube)

(Cube Root)

‡

(Root)

‡

(cube,

MATH MATH

, item 3) returns the cube of a number,

expression, or list.

value

‡

(cube root,

MATH MATH

number, expression, or list.

value

‡

(root,

MATH MATH

, item 5) returns the

number, expression, or list.

root

value

‡

, item 4) returns the cube root of a

real root of a

2-8 Math, Angle, and Test Operations

NDERIV(

(numerical derivative,

MATH MATH

, item 6) returns an approximate derivative of an expression with respect to a specified variable, given the value at which to calculate the

derivative, and H (optional; if none is specified, 1

NDERIV( NDERIV(

NDERIV(

expression,variable,value expression,variable,value,H

uses the symmetric difference quotient method (as

)

3 is used).

shown in the formula below), which approximates the numerical derivative value as the slope of the secant line through the points:

) =

f¢(

+H)–f(X–H)

As H gets smaller, the approximation usually gets more accurate.

Because of the method used,

NDERIV(

can return a false

derivative value at a nondifferentiable point.

Math, Angle, and Test Operations 2-9

MATH NUM (Number) Operations

To display the MATH NUM menu, press the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.

MATH NUM Menu

ROUND(

MATH NUM PRB 1: ROUND( 2: IPART 3: FPART 4: INT 5: MIN( 6: MAX( 7: REMAINDER(

ROUND( (MATH NUM

I 9

. When you select a menu item,

Round. Integer part. Fractional part. Greatest integer. Minimum value. Maximum value. Remainder of a division result.

, item 1) returns a number, expression, or list rounded to a specified number of decimals (9). If the number of decimals is omitted, the number is rounded to the digits that are displayed, a maximum of 10 digits.

PART

FPART

value,#decimals

Round(

PART

(integer part,

) Round(

MATH NUM

part or parts of a number, expression, or list. (fractional part,

MATH NUM

, item 3) returns the fractional

value

)

, item 2) returns the integer

FPART

part or parts of a number, expression, or list.

PART

value

FPART

value

(greatest integer,

INT

integer less than or equal to a number, expression, or list. The value is the same as

negative integers, but one integer less than noninteger numbers.

value

INT

2-10 Math, Angle, and Test Operations

MATH NUM

PART

, item 4) returns the largest

for nonnegative numbers and

PART

for negative

MIN( MAX(

(minimum value,

MIN(

MATH NUM

, item 5) returns the smaller of two values or the smallest element in a list. If two lists are compared, it returns a list of the smaller of each pair of elements. If a list and a value are compared, it compares each element in the list to the value.

(maximum value,

MAX(

MATH NUM

, item 6) returns the larger of two values or the largest element in a list. If two lists are compared, it returns a list of the larger of each pair of elements. If a list and a value are compared, it compares each element in the list to the value.

valueA,valueB

MIN(

list

MIN(

listA,listB

MIN(

value,list

MIN(

list,value

MIN(

) MAX(

) MAX( ) MAX( ) MAX(

valueA,valueB list

)

listA,listB value,list list,value

) ) )

)

REMAINDER(

Note:

MIN(

and

are also available on the

MAX(

LIST MATH

menu.

REMAINDER( (MATH NUM

, item 7) returns the remainder resulting from the division of two integers, each of which can be a list. (See

REMAINDER( REMAINDER(

, page 2–7.)

INT÷

valueA,valueB value,list

) REMAINDER(

listA,listB list,value

)

If a list is used as one or both arguments, the result is a list of remainders.

Math, Angle, and Test Operations 2-11

MATH PRB (Probability) Operations

To display the MATH PRB menu, press the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.

MATH PRB Menu

RAND

MATH NUM PRB 1: RAND 2: nPr 3: nCr 4: ! 5: RANDINT(

(random number,

RAND

I 6

. When you select a menu item,

Random number generator. Number of permutations. Number of combinations. Factorial. Random integer generator.

MATH PRB

, item 1) generates and returns a random number greater than 0 and less than 1 (as in the first example below). A random number is generated from a seed value. To control a random number sequence, first store an integer seed value in below,

is stored to

so that the TI-80 uses 1 as the seed

RAND

. In the second example

RAND

value for generating random numbers.

Note: When you reset the TI-80,

is set to the factory

RAND

seed value, which is 0.

2-12 Math, Angle, and Test Operations

nPr nCr

(Factorial)

(number of permutations,

nPr

number of permutations of

items

and

nCr

number

and

number

must be nonnegative integers. Both

can be lists.

(number of combinations,

number of combinations of

items

and

items items

(factorial,

and

number

nPr nCr

number

can be lists.

number number

MATH PRB

must be nonnegative integers. Both

, item 4) returns the factorial of a

MATH PRB

items

MATH PRB

items

, item 2) returns the

number

taken

, item 3) returns the

number

taken

positive integer or list of integers between 0 and 69.

value

at a time.

items

at a time.

items

RANDINT(

(random integer,

MATH PRB

, item 5) generates a random integer within a specified range. It requires two arguments: the lower and upper boundaries of the range (in any order). Both arguments must be integers. Both arguments can be negative. Both arguments can be lists.

RANDINT(

lower,upper

)

Math, Angle, and Test Operations 2-13

ANGLE Operations

To display the ANGLE menu, press indicators and instructions. When you select an item from the menu, the name is copied to the cursor location.

ANGLE Menu

(Degree)

ANGLE 1:

2: 3: R8Pr( 4: R8Pq( 5: P8Rx( 6: P8Ry(

(degree,

2 E

. The ANGLE menu displays angle

Degree notation. Radian notation. Returns r, given X and Y. Returns q, given X and Y. Returns x, given R and q. Returns y, given R and q.

, item 1) lets you designate an angle or list of

ANGLE

angles as degrees, regardless of the current angle mode setting. In

RADIAN

mode, ¡ can also be used to convert

degrees to radians.

value

Mode

(Radians)

(radians,

RADIAN

, item 2) lets you designate an angle or list

ANGLE

of angles as radians, regardless of the current angle mode setting. In

DEGREE

mode, r can also be used to convert

radians to degrees.

value

DEGREE

Mode

2-14 Math, Angle, and Test Operations

R8Pr( R8Pq( P8Rx( P8Ry(

Note: When converting from one coordinate system to the other, be sure that the angle mode setting,

RADIAN

R8Pr( (ANGLE

, is appropriate for your angle measurements. (Press

to check the current setting.)

, item 3) converts the given rectangular

DEGREE

coordinates to polar coordinates and returns

R8Pq( (ANGLE

, item 4) converts the given rectangular

coordinates to polar coordinates and returns

Both X and Y can be lists.

R8Pr(X,Y)

X,Y

R8Pq( RADIAN

P8Rx(

to rectangular coordinates and returns

P8Ry( (ANGLE

to rectangular coordinates and returns

)

Mode

(

ANGLE

, item 5) converts the given polar coordinates

, item 6) converts the given polar coordinates

Both R and q can be lists.

P8Rx(R,q)

P8Ry(

,q)

RADIAN

Mode

Math, Angle, and Test Operations 2-15

TEST (Relational) Operations

To display the TEST menu, press 2 D. When you select from the menu, the name is copied to the cursor location. These functions are valid for lists; they return a list calculated on an element-by-element basis.

TEST Menu

‚



Using Tests

TEST 1:= 2: 3:> 4: 5:< 6:

Relational operators compare if the test is true or 0 if the test is false.

True if:

Equal.

Not equal to. Greater than.

‚

Greater than or equal to. Less than.



Less than or equal to.

valueA

and

valueA

valueB

and

and return

valueB

be numbers, expressions, or lists.

Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.

valueA valueA valueA valueA valueA valueA

valueB

‚

valueB



Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1).

The expression

2+2=2+3

returns 0. The TI-80 does the addition first because of EOS rules, and then it compares 4 to 5.

The expression

2+(2=2)+3

returns 6. The TI-80 first performs the relational test because it is in parentheses; then it adds 2, 1, and 3.

can

2-16 Math, Angle, and Test Operations

Chapter 3: Fractions

This chapter describes how to use the fraction operations on the TI.80.

Chapter Contents

Getting Started: Working with Fractions Setting Modes for Fraction Results

.............

..................

Entering and Using Fractions in Calculations The

FRACTION

..............................

.........

3-2 3-4 3-6 3-8

Fractions 3-1

Getting Started: Working with Fractions

Getting Started is a fast-paced introduction. Read the chapter for details. Enter the expression 1

and then use the conversion options on the FRACTION menu to convert the result.

This example is performed in

6/27

+ 1

Evaluate the expression, simplify the result,

1/9.

MANSIMP

(manual simplification) mode.

MANSIMP

mode is especially useful for students when they are learning fraction concepts. When

MANSIMP

mode is selected, the

function (from the

SIMP

FRACTION

menu) can be used to simplify fractions step-by-step.

1. Select

MANSIMP

2. From the Home screen, press 1 2 « 1 2

fraction expression,

3. Press

mode.

1 2 _ 9 to enter the mixed-

+ 1

1/9

6/27

to evaluate the expression. The

6 2

indicates that the fraction can be simplified.

4. Press

1 to select

SIMP

simplify).

(

ANSúSIMP

is copied to the cursor location.

MANSIMP

to simplify the fraction.

mode, the TI-80 uses the lowest

5. Press

common factor for simplification. The simplification factor is displayed. The

preceding the result indicates that the fraction can be simplified further. Continue pressing

until

is no longer

displayed.

3-2 Fractions

The TI.80 uses the lowest common factor for simplification. If you want to choose the simplification factor yourself, you can enter it as part of the expression.

6. Press

to clear the screen. Reenter the expression, or press 2 expression

+ 1

6º27

1º9

until you see the

7. Press 2 6 2 / c 2 9 b 9 d. This adds the simplification factor 9 and places the expression in parentheses.

8. Press

9. Press

1 to copy

to simplify the fraction result. The

to the cursor location.

SIMP

simplification factor is displayed.

10. Press 2 ±

to convert the mixed

fraction result to a simple fraction.

11. Press 2 ±

result to its decimal equivalent.

to convert the fraction

Fractions 3-3

Setting Modes for Fraction Results

From the MODE screen, you can select simplification and display format options for fraction results.

AUTOSIMP Mode with bºc and aÀbºc Modes

AUTOSIMP

mode simplifies fractions automatically. Simplification takes place before the expression is evaluated. Then the result is simplified to its lowest terms. For example,

is simplified to

12à16

when you press

3à4

There are two formats for displaying fractions results.

mode displays fraction results in simple-fraction (a

bºc

fraction without a whole number) format; for example,

25à4

displays fraction results in mixed-fraction (a whole

aÀbºc

number with a fraction) format; for example

3/4

3-4 Fractions

MANSIMP Mode with aÀbºc Mode

MANSIMP MANSIMP

concepts. In

mode lets you simplify fractions manually. was designed for teaching and learning fractions

MANSIMP

mode, you can simplify fractions and

the results of expressions using fractions, step-by-step.

When a fraction result is not expressed in its lowest terms, a down arrow ( simplify the result. Use simplify the fraction. You can then use

) is displayed to remind you that you can

from the

SIMP

FRACTION

úbº

úaÀbº

menu to

change the display format of the fraction result.

Typically, you use the

úaÀbº

display format mode for teaching or learning fraction

MANSIMP

simplification mode with the

concepts. The display format of fraction results can vary when you are using

When you simply enter a fraction and press

MANSIMP

and

úaÀbº

, the

format in which you entered the fraction is preserved.

When you add or subtract using a mixed fraction, calculation takes place on the whole-number and fractional part of the mixed-fraction separately. The result is displayed as a mixed fraction.

When you multiply or divide using a mixed fraction, the result is displayed as a simple fraction.

Fractions 3-5

Entering and Using Fractions in Calculations

The TI.80 lets you enter fractions directly from the keyboard.

Entering Simple Fractions

Entering Mixed Fractions

A simple fraction is a fraction with no whole-number part; for example,

3à4

4à3

To enter a simple fraction:

1. Enter the numerator (up to six digits), and then press

2. Enter the denominator (up to and including 1000).

For example, press

2 _ 3 to enter

2à3

A mixed fraction is fraction that has both a whole-number and a fractional part; for example

1à3

To enter a mixed fraction:

1. Enter the units (up to three digits), and then press

2. Enter the numerator (up to three digits), and then press

2 _

3. Enter the denominator (up to and including 1000).

For example, press

2 2 _ 3 to enter

2à3

3-6 Fractions

In general, you can use fractions in expressions just as you would use other numbers. The results of the expressions, however, may or may not be fractions.

Using Fractions in Expressions

The absolute value of a fraction on the TI

«, |, p, e, V, a, ·

, and 2 P accept fraction entries

80 cannot be ≥1000.

and return fraction results. If the absolute value of a fraction

result is ≥1000, or if the results of operations with these

functions are not within the limits shown on page 3-6, the results are given in decimal form.

Other functions accept fraction entries, but convert them to decimal form before operating on them. The results are given in decimal form. For example,

2à3

If you use

with a fraction that has been converted to a

SIMP

‡4à

returns

.6666666667

, not

decimal, an error occurs.

If an expression contains both a fraction and a decimal number, the result is displayed as a decimal number.

You can also enter fractions in a list, but the results are returned as decimal values.

Fractions 3-7

The FRACTION Menu

To display the FRACTION menu, press J. The menu items let you simplify and convert fractions. When you select a menu item, the name is copied to the cursor location.

FRACTION Menu

Simplifying Fractions

SIMP

FRACTION 1:8SIMP 2:8bºc 3:8aÀbºc 4:8FRAC 5:8DEC

SIMP

Simplifies the fraction. Converts to a simple fraction. Converts to a mixed fraction. Converts a decimal to a fraction based on mode. Converts a fraction to a decimal.

(simplify fraction,

FRACTION

, item 1) simplifies the specified fraction and displays it, along with the simplification factor.

Note:

can only be used in

SIMP

MANSIMP

mode.

You have two options for simplifying fractions.

You can let the calculator simplify the fraction, step-bystep, using the lowest common factor (LCF).

fraction

You can choose a factor (an integer) for simplifying the

SIMP

fraction.

fraction,factor

(

)úSIMP

3-8 Fractions

Both simplification options update the variable

FACTOR

Converting Simple and Mixed Fractions

úbº

aÀbºc

(convert to simple fraction,

bºc

value

to a simple fraction.

(convert to mixed fraction, item 3) converts

aÀbºc

FRACTION

mixed fraction.

value

bºc

value

aÀbºc

, item 2) converts

value

to a

Both

bºc

and

expression. A

can be used only at the end of an

aÀbºc

! (§

) instruction, however, can follow them.

Fractions 3-9

Converting Decimals and Fractions

FRAC

DEC

(convert to fraction,

FRAC

decimal decimal

value to its fraction equivalent and displays it. The may be a number, expression, or list.

MANSIMP

mode,

FRACTION

first attempts to return a fraction

FRAC

, item 4) converts a

in terms of 10ths, 100ths, or 1000ths. If this is not possible,

converts the decimal to its fraction equivalent as it

FRAC

would in

AUTOSIMP

mode. If the value cannot be converted or if the denominator of the equivalent fraction is greater than 1000, the decimal equivalent is returned.

The form of the display format. For example,

is selected or

aÀbºc

decimal

If the

FRAC

5à4

value for

result depends on the current fraction

FRAC

returns

1.25

is selected.

bºc

is a list, the list is displayed as

FRAC

1à4

fractions, but it is still stored internally in decimal form.

(convert to decimal,

DEC

fraction

decimal fraction

AUTOSIMP & aÀbºc AUTOSIMP & bºc

MANSIMP & aÀbºc MANSIMP & bºc

value to its decimal form and displays it.

FRAC

DEC

FRACTION

, item 5) converts a

3-10 Fractions

Both

FRAC

expression. A

and

(§) instruction, however, can follow them.

are valid only at the end of an

DEC

Chapter 4: Function Graphing

This chapter describes function graphing on the TI.80 in detail. It also lays the foundation for using the parametric graphing features described in Chapter 5.

Chapter Contents

Getting Started: Graphing a Circle Defining a Graph Setting Graph Modes Defining Functions in the Evaluating Selecting Functions

..................................

..............................

Functions in Expressions

...............................

Defining the Viewing Window Displaying a Graph

................................

...................

....................

List

.............

......................

Exploring a Graph with the Free-Moving Cursor Exploring a Graph with Exploring a Graph with Setting the Zoom Factors

.....................

TRACE

......................

ZOOM

..........................

......

4-2 4-3 4-4 4-5 4-7 4-8

4-9 4-11 4-12 4-13 4-15 4-18

Function Graphing 4-1

Getting Started: Graphing a Circle

Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing

window. To graph a circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSQUARE to adjust the display to make the functions appear as a circle.

Make sure that your TI-80 is in

STAT PLOTS

are turned off.

FUNC

mode and all

1. Press ( to display the Y= edit screen. Press 2

| @ a d

100

Y1=‡(100–X2)

to enter the expression

, which defines the top half of the

circle.

The bottom half of the circle is defined by

Y2=‡(100–X2)

. However, you can also define

one function in terms of another; so to define

, press · 2

Y2=LY1

variables menu)

2. Press

6 to select

(to select Y1).

ZSTANDARD

(to display the

. This is a quick

way to reset the Window variables to the standard values. It also graphs the functions; you do not need to press

Notice that the functions appear as an ellipse in the standard viewing window.

3. To adjust the display so each “dot” represents an equal width and height, press select

ZSQUARE

. The functions are replotted and

, and then

now appear as a circle on the display.

4. To see the

)

and notice the values for

and

YMAX

ZSQUARE

Window variables, press

XMIN, XMAX, YMIN

]

5. If you want to see the graph again, press

4-2 Function Graphing

Defining a Graph

To define a graph, you set the modes, enter and select the functions to graph, and define the viewing window and the graphing format. Once you have defined a graph, you can plot it, display it, and explore it.

Steps in Defining a Graph

Exploring a Graph

There are six basic steps to defining a graph, although you may not need to do all of the steps each time you define a graph. The procedures are described in detail on the following pages.

1. Set the mode to

graphing (Chapter 1).

FUNC

2. Enter or edit a function in the Y= list (page 4-5).

3. Select the Y= function you want to graph (page 4-8).

4. Define the viewing window (page 4-9).

5. Set the graphing format (page 4-11).

6. Deselect

STAT PLOTS

, if appropriate (Chapter 9).

Once you have defined a graph, you can display it and use several tools on the TI-80 to explore the behavior of the function or functions. These tools are described later in this chapter.

Function Graphing 4-3

Setting Graph Modes

Pressing 3 displays the current mode settings, as described in Chapter 1. For function graphing, the graphing mode must be set to FUNC. Before you graph a function, check to be sure that the mode settings are appropriate.

Checking and Changing Graphing Modes

Setting Modes from a Program

Press 3 to display the mode settings. The current settings are highlighted.

The TI-80 has two graphing modes.

To graph functions, you must select

(function graphing)

FUNC

(parametric graphing)

PARAM

FUNC

(function

graphing).

The basics of graphing on the TI-80 are described in this chapter. Differences in parametric graphing are described in Chapter 5.

The mode settings can affect how functions are graphed.

RADIAN

DEGREE

mode may affect how some functions

are interpreted.

CONNECTED

affects how the selected functions

DOT

are plotted.

SEQUENTIAL

affects how functions are plotted

SIMUL

if you have more than one function selected.

You can set the graphing mode and other modes from a program.

Begin on a blank line in the program editor. Press 3 to display the on the mode that you want to select, and then press

screen. Press 8 and 7 to place the cursor

MODE

The name of the mode is copied to the cursor location.

4-4 Function Graphing

Defining Functions in the Y= List

Pressing ( displays the Y= edit screen. This is where you enter the functions to graph. You can store up to four functions in memory at one time. You can graph one or more of these functions at a time.

Displaying the Functions in the Y= List

Defining a New Function

Press ( to display the Y= edit screen. In the example below, the

and Y2 functions are defined.

To define a new function in the Y= list:

1. Press ( to display the Y= edit screen.

2. Move the cursor to the function in the Y= list you want to define. If necessary, press

to erase a previously

entered function.

3. Enter the expression to define the function.

You may use functions and variables in the expression. If the expression evaluates to a value that is not a real number, that point is not plotted; an error does not occur.

The independent variable in the function is X. You may

press @, rather than pressing variable. ( as

The expression is stored as one of the four user-defined functions in the

mode defines the independent variable

FUNC

list as you enter it.

, to enter the

Note: You can use a list within a Y= function; however, the function must evaluate to a single value.

4. When you complete the expression, press

to move

to the beginning of the next function.

Note: When you enter a function, it is automatically selected for graphing in the

list. This is indicated by the highlighted

equal sign. For details on selecting and deselecting functions, see page 4-8.

Function Graphing 4-5

Editing a Function

Clearing a Function

Defining Functions from the Home Screen or a Program

To edit a function in the

list:

1. Press ( to display the Y= list, and move the cursor to the function you want to change.

2. Make the changes. You can also press

to erase the

expression, and then enter a new expression.

The expression is stored in the

list and selected (turned

on) as you edit it.

To clear or erase a function on the cursor anywhere on the function, and then press

edit screen, position the

To define a function from the Home screen or from a program, begin on a blank line.

again.

, enter the expression, and then press

1. Press

2. Press §.

3. Press 2 from the

, and then select the name of the function

menu. The name is copied to the cursor

location.

4. Press

expression

to complete the instruction.

"!Y

When the instruction is executed, the TI-80 stores the expression in the displays the message

Leaving the Y= Edit Screen

To leave the

4-6 Function Graphing

list, selects (turns on) the function, and

DONE

edit screen:

Select another screen by pressing the appropriate key, such as

)

Press 2 . to return to the Home screen.

Evaluating Y= Functions in Expressions

You can the calculate the value of a Y= function at a specified value of X.

Entering the Functions in the Y= List



Evaluating Functions



Evaluating Functions without Parentheses



To display the Y= list, press (. Enter these functions for Y1,

, and Y3:

@ a

@ «

2 G

@ d d

To evaluate the functions, first specify the value of X. Note that X may be a list.

2 . M 2 G

2 G

You can also evaluate functions without using parentheses by storing a value to X.

§ @

2 G

1 c 2

X+2

c 2 G

c 2 [

, and

Y1(Y2(X))

, 2 , 3

2 2

c 3

2 \

Function Graphing 4-7

Selecting Functions

Only functions that are selected (turned on) are graphed. All four functions may be selected at one time.

Turning a Function “On” or “Off”

Selecting Functions from the Home Screen or a Program

You can select and deselect (“turn on” and “turn off”) functions on the

edit screen. The = sign on a selected

function is highlighted.

To change the selection status of a function:

1. Display the

list, and move the cursor to the function

whose status you want to change.

2. Press 6 to place the cursor over the

3. Press

to change the status. If the function was

sign of the function.

selected, it is now deselected. If it was deselected, it is now selected.

Note: When you enter or edit a function, it is selected automatically. When you clear a function, it is deselected.

To select functions from the Home screen or a program, begin on a blank line.

1. Press 2

ON/OFF

2. Select the instruction you want,

, and then press 6 to select

menu is displayed.

FNON

ON/OFF

FNOFF

. The

. It is

copied to the cursor location.

3. To turn specific functions on or off, enter the number(s) of the function(s), separated by commas.

function#

FNON

function#

FNOFF

For example, in

and Y3.

function#

mode,

FUNC

. . .

FNOFF 1,3

turns off functions

4-8 Function Graphing

Defining the Viewing Window

The Window variables determine the boundaries and other attributes of the viewing window. The Window variables are shared by all graphing modes.

The Viewing Window

Checking the Viewing Window

Changing a Window Variable Value

The viewing window of the TI-80 is the portion of the coordinate plane defined by

XMIN, XMAX, YMIN

The distance between tick marks is defined by axis and

XMIN

)

Press

for the Y axis.

YSCL

YMAX

XSCL

XMAX

YSCL

YMIN

to display the current Window variable values.

, and

XSCL

YMAX

for the

The values shown here are the default values.

To change a Window variable value:

1. Press 8 to move to the Window variable you want to change.

2. To enter a real value (which can be an expression), you may do any of the following:

Position the cursor, and then make the changes.

Press

to clear the value, and then enter a new

value.

Begin entering a new value. The original value is cleared automatically when you begin typing.

3. Press

¸, 8

, or 7. If you entered an expression, it is

evaluated. The new value is stored.

must be less than

XMIN

, or you will get an error message when you press

YMAX

. To turn off the tick marks, set

XMAX

, and

must be less than

YMIN

XSCL=0

and

YSCL=0

Function Graphing 4-9

Leaving the Window Screen

Storing to a Window Variable from the Home Screen or a Program

X and @Y

To leave the Window screen:

Select another screen by pressing the appropriate key,

such as

Press 2 . to return to the Home screen.

or (.

To store to a Window variable from the Home screen or from a program, begin on a blank line.

1. Enter the value (which can be an expression) that you want to store.

2. Press §.

3. Press

4. Select

to display the

WINDOW...

menu.

VARS

to display the Window variables.

5. Select the Window variable. The name of the variable is copied to the cursor location.

6. Press

to complete the instruction.

Note: You can use a Window variable in an expression by performing steps 3, 4, and 5.

The variables

and

define the distance between the

centers of two adjoining pixels on a graph (graphing accuracy).

(

XMAX – XMIN

and

are not on the Window screen; however, they are

accessible through the calculated from

)(

62 46

VARS WINDOW...

XMIN, XMAX, YMIN

YMAX – YMIN

menu.

, and

YMAX

when a graph

and

)

are

is displayed.

You can store values directly to

VARS WINDOW...

immediately calculated from

menu), in which case

XMIN

and

(7 and 8 on the

XMAX

, and

and

YMIN

YMAX

are

4-10 Function Graphing

Displaying a Graph

Pressing mode settings apply, and the current values of the Window variables define the viewing window.

Turning the Grid Points On and Off

Displaying a New Graph

graphs any functions selected on the Y= edit screen. The current

Grid points correspond to the axis tick marks. To turn the grid points on and off use the TI-80 is

GRIDOFF

GRIDON

1. From the Home screen, press 2

menu.

DRAW

2. Press 9 to select

3. Press

Press

GRIDON

. The message

to display the graph of the selected function or

functions. (Some operations, such as

and

GRIDOFF

. The default for

to display the

, or press 0 to select

is displayed.

DONE

and the Zoom

TRACE

GRIDOFF

instructions, display the graph automatically.) As a graph is

Smart Graph

plotted, the busy indicator is on, and

When you press

, Smart Graph displays the graph

and Y are updated.

screen immediately if nothing has changed that requires the functions to be replotted since the last time the graph was displayed.

If you have changed any of the following since the graph was last displayed, pressing

replots the graph based on the

new values.

Changed a mode setting that affects graphs.

Changed a function in the current picture.

Deselected a function in the current picture.

Changed the value of a variable in a selected function.

Changed a Window variable or format setting.

Cleared drawings by selecting

Changed or turned off a

CLRDRAW

STAT PLOT

(Chapter 7).

definition (Chapter

9).

Overlaying Functions on a Graph

Note:

CLRDRAW

The TI-80 lets you graph one function at a time without replotting every function. For example, enter

press

is a fast way to replot a graph.

. Then enter

COS X

SIN X

and press

and

again.

The second function is graphed on top of the original function.

Function Graphing 4-11

Exploring a Graph with the Free-Moving Cursor

While a graph is displayed, you can move the free-moving cursor anywhere on the graph and display the coordinates of any location on the graph.

Free-Moving Cursor

Graphing Accuracy

You can press 6, 9, 7, or 8 to move the cursor around the graph. When you first display the graph, no cursor is visible. As soon as you press 6, 9, 7, or 8, the cursor moves from the center of the viewing window.

As you move the cursor around the graph, the values of the variables

and Y are updated, and the coordinate values of

the cursor location are displayed at the bottom of the screen. Coordinate values generally appear in floating-decimal format. The numeric display settings on the

MODE

screen do not

affect coordinate display.

To see the graph without the cursor or coordinate values, press

. When you press 6, 9, 7, or 8, the

cursor begins to move from the same position.

The free-moving cursor moves from dot to dot on the screen. When you move the cursor to a dot that appears to be “on” the function, it may be near, but not on, the function; therefore, the coordinate value displayed at the bottom of the screen is not necessarily a point on the function. To move the cursor along a function, use

TRACE

(page 4-13).

The displayed coordinate values of the free-moving cursor approximate actual math coordinates accurate to within the width/height of the dot. As

) get closer together (after a

YMAX

XMIN

and

ZOOM IN

XMAX

(and

YMIN

and

, for example), graphing accuracy increases, and the coordinate values more closely represent the math coordinates.

4-12 Function Graphing

Free-moving cursor “on” the curve

)

Exploring a Graph with TRACE

TRACE moves the cursor from one plotted point to the next along a function. The cursor coordinates are displayed at the bottom of the screen.

Beginning a Trace

Moving along a Function

Press already, the TI-80 displays it. The cursor is on the first selected function in the screen. The number of the function appears at the upper right of the display.

Note: If any trace the first stat plot.

Press 9 and 6 to move the cursor along the function. Each press moves the cursor from one plotted point to the next. Press 2 9 and 2 6 to move the cursor five plotted points at a time. Tracing updates and displays the values of the variables that is,

value is blank.

to begin a trace. If the graph is not displayed

list at the middle X value on the

STAT PLOTS

and Y. The Y value is calculated from the X value;

Y=Yn(X)

. If the function is undefined at an X value, the

are turned on, the TI-80 attempts to

Trace cursor on the curve.

)

Panning to the Left or Right

QuickZoom

If the Y value of a function is above or below the viewing window, the cursor disappears as you move it to that portion of the function. However, the coordinate values at the bottom of the screen indicate the cursor coordinates.

If you trace a function off the left or right edge of the screen, the viewing window automatically pans to the right or left.

XMIN

and

are updated to correspond to the new

XMAX

viewing window.

Note: The screen does not pan if a

While tracing, you can press

STAT PLOT

to adjust the viewing

is on.

window so that the cursor location becomes the center of a new viewing window, even if the cursor is above or below the display. This allows “panning” up and down. After QuickZoom,

TRACE

is still active.

Function Graphing 4-13

Moving from Function to Function

Leaving TRACE

Using TRACE in a Program

To trace another selected function on the graph, press 8 or to move the cursor to that function. The cursor moves to the new function at the same

value. The function number in the

upper right corner of the display changes.

The cursor movement is based on the order of the selected functions in the

list, not the appearance of the functions as

graphed on the screen.

To leave

Select another screen by pressing the appropriate key, such as

Press

TRACE

)

to see the graph without the Trace

cursor.

Press 2 . to return to the Home screen.

The Trace cursor remains in the same location if you leave

and return, as long as Smart Graph has not caused the

TRACE

graph to be replotted.

On a blank line in the program editor, press instruction

is copied to the cursor location. When the

Trace

. The

instruction is encountered during program execution, the graph is displayed with the Trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the function(s), press

to resume program execution.

4-14 Function Graphing

Exploring a Graph with ZOOM

Pressing the graph quickly in a variety of ways. All of the Zoom instructions are accessible from programs.

ZOOM Menu

ZBOX

displays a menu that allows you to adjust the viewing window of

ZOOM 1: ZBOX 2: ZOOM IN 3: ZOOM OUT 4: ZDECIMAL 5: ZSQUARE 6: ZSTANDARD 7: ZTRIG

lets you use the cursor to select opposite corners of a

ZBOX

Draws box to define viewing window. Magnifies graph around cursor. Views more of graph around cursor. Sets .1 as dot size. Sets equal sized-dots on X and Y axes. Sets standard Window variables. Sets built-in trig Window variables.

box to define a new viewing window.

1. Select

ZBOX

from the

menu. The different cursor at

ZOOM

the center of the screen indicates that you are using a Zoom instruction.

2. Move the cursor to any corner of the box you want to

define, and then press

. As you move the cursor away from the point just selected, you see a small square dot, indicating that the first corner is selected.

3. Move the cursor to the diagonal corner of the box you want to define. As you move the cursor, the boundaries of the box change on the screen.

Note: Before you press can cancel pressing

at any time by

ZBOX

, you

4. When the box is defined as you want it, press replot the graph.

You can repeat steps 2 through 4 to do another

ZBOX

Function Graphing 4-15

ZOOM IN ZOOM OUT

Leaving ZOOM IN or ZOOM OUT

ZOOM IN XFACT

(page 4-18). The default value for both

magnifies the graph around the cursor location. The

and

settings determine the extent of the zoom

YFACT

XFACT

and

YFACT

1. After checking or changing

ZOOM IN

from the

ZOOM

menu.

XFACT

and

YFACT

, select

Notice the different cursor. It indicates that you are using a Zoom instruction.

2. Move the cursor to the point that you want as the center of

the new viewing window, and then press

The TI-80 adjusts the viewing window by

, updates the Window variables, and replots the

YFACT

XFACT

and

selected functions centered on the cursor location.

ZOOM IN

is still turned on. To zoom in on the graph again:

At the same point, press

At a new point, move the cursor to the point that you want as the center of the new viewing window, and then

press

ZOOM OUT

displays a greater portion of the graph, centered on the cursor location, to provide a more global view. The procedure for

To leave

Select another screen by pressing the appropriate key, such as

Press 2 . to return to the Home screen.

ZOOM OUT

ZOOM IN

is the same as for

ZOOM OUT

ZOOM IN

4-16 Function Graphing

ZDECIMAL

Window variables to preset values that set

, and defines the X and Y value of each pixel as one decimal.

.1 XMIN = L3.1 YMIN = L2.3

XMAX = 3.1 YMAX = 2.3 XSCL = 1 YSCL = 1

replots the functions immediately, updates the

and

equal to

ZSQUARE

ZSTANDARD

ZTRIG

ZSQUARE

replots the functions immediately, redefining the

window based on the current Window variables, but adjusted

XSCL

@X=@

. This makes the graph of a

and

remain unchanged.

YSCL

in only one direction so that circle look like a circle. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.

ZSTANDARD

replots the functions immediately, updating the

Window variables to the standard values:

XMIN = L10 YMIN = L10 XMAX = 10 YMAX = 10 XSCL = 1 YSCL = 1

replots the functions immediately, updating the

ZTRIG

Window variables to preset values appropriate for plotting trig functions. In

XMIN = L(31/12)p (L8.115781..) YMIN = L2 (L2) XMAX = (31/12)p (8.1157810..) YMAX = 2 (2) XSCL = (p/2) (1.5707963..) YSCL = 1 (1)

RADIAN

mode, these are:

Function Graphing 4-17

Setting the Zoom Factors

The Zoom factors, XFACT and YFACT, determine the extent of the change for the viewing window created by ZOOM IN or ZOOM OUT on a graph.

Zoom Factors

Checking Zoom Factors

Setting Zoom Factors from the Home Screen or a Program

Zoom factors are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to

ZOOM IN

ZOOM OUT

around a

point.

To review the current values of the Zoom factors (

YFACT

1. Press

2. Press 9 to select

3. Press

, and then press

XFACT

is copied to the cursor location.

YFACT

. The Zoom factor is displayed.

To set the Zoom factors

XFACT

to select

or 0 to select

and

YFACT

WINDOW...

YFACT. XFACT

from the Home

XFACT

and

screen or a program, begin on a blank line.

1. Enter the factor, and then press §.

2. Press

3. Press 9 to select

, and then press

XFACT

is copied to the cursor location on the Home

YFACT

to select

or 0 to select

WINDOW...

YFACT. XFACT

screen.

4. Press

to store the Zoom factor to the variable.

4-18 Function Graphing

Chapter 5: Parametric Graphing

This chapter describes how to graph parametric equations on the TI.80. Before doing parametric graphing, you should be familiar with Chapter 4, Function Graphing.

Chapter Contents

Getting Started: Path of a Ball

......................

Defining and Displaying a Parametric Graph Exploring a Parametric Graph

......................

..........

5-2 5-3 5-6

Parametric Graphing 5-1

Getting Started: Path of a Ball

Getting Started is a fast-paced introduction. Read the chapter for details.

Graph the parametric equation that describes the path of a ball kicked at an angle of 60¡ with an initial velocity of 15 meters per second. (Ignore air resistance.) What is the maximum height? When does the ball strike the ground?

1. Press 3, and then press 8 8 8 8 8 9 select

PARAM

mode.

For initial velocity v0 and angle q, the horizontal component of the ball as a function of time is X(t) = t v Y(t) = t v

9.8 màsec

2. Press (. Press 15 @ X 60 2

)

equation in terms of

3. Press 15 @ W 60 2

9.8

4. Press

cos q. The vertical component is

sin q -(gà2) t2. The gravity constant g is

to define the X portion of the parametric

1 (to select ¡) |

e 2 d @ a

)

to define the Y portion.

. Enter the Window variables

1 (to select

appropriate for this problem.

TMIN=0 XMIN=ë2 YMIN=ë2 TMAX=3 XMAX=25 YMAX=10 TSTEP=.2 XSCL=5 YSCL=5

5. Press

to graph the position of the ball as a

function of time.

Tracing begins at

. As you press 9~ to trace the

TMIN

curve, the cursor follows the path of the ball over time. The values for

(distance), Y (height), and

(time) are displayed at the bottom of the screen.

The maximum height is approximately 8.6 meters. The ball strikes the ground in approximately 2.6 seconds.

5-2 Parametric Graphing

Defining and Displaying a Parametric Graph

Parametric equations consist of an X component and a Y component, each expressed in terms of the same independent variable T. They are often used to graph equations over time. Up to three pairs of parametric equations can be defined and graphed at a time.

Defining a Parametric Graph

Setting Parametric Graph Modes

Displaying Parametric Equations

Defining Parametric Equations

The steps for defining a parametric graph are the same as those for defining a function graph (page 4-3). Differences are noted below.

Press 3 to display the mode settings. To graph parametric equations, you must select

PARAM

before you enter Window variables or enter the components of parametric equations. Normally, you should also select

CONNECTED

to obtain a

more meaningful parametric graph.

After selecting parametric

edit screen.

On this screen, you display and enter both the X and

mode, press ( to display the

PARAM

components. The TI-80 allows three parametric equations, each defined in terms of

Follow the same procedures as for function graphing (pages 4-5 to 4-6) to enter the two components that define a new parametric equation.

You must define both the X and Y components in a pair.

The independent variable in each component is T. You

may press @, rather than pressing parametric variable independent variable as

. (

PARAM

, to enter the

mode defines the

Parametric Graphing 5-3

Selecting Parametric Equations

Setting Window Variables

The TI-80 graphs only the parametric equations you select. The highlighted = sign on both components of an equation indicates that the equation is selected.

You may select any or all of the equations on the parametric

edit screen.

To change the selection status of a parametric equation, press

to move the cursor onto the

component and press

sign of either the X or

. The status on both the X and

components changes.

Note: When you enter both components of an equation or edit either component, that equation is selected automatically.

)

Press

to display the current Window variable values. The Window variables define the viewing window. The values shown are the standard values in

RADIAN

mode.

TMIN=0 TMAX=6.283185307 TSTEP=.1308996938996 XMIN=L10 XMAX=10 XSCL=1 YMIN=L10 YMAX=10 YSCL=1

Smallest T value to evaluate. Largest T value to evaluate. T value increment. Smallest X value to be displayed. Largest X value to be displayed. Spacing between X tick marks. Smallest Y value to be displayed. Largest Y value to be displayed. Spacing between Y tick marks.

To change a Window variable value, follow the steps given for function graphing (page 4-8).

Note: You may want to change the T variable values to ensure that sufficient points are plotted.

5-4 Parametric Graphing

Displaying a Graph

VARS WINDOW and Y-VARS Menus

When you press parametric equations. It evaluates both the X and the component for each value of T (from intervals of

, the TI-80 plots the selected

TMIN

) and then plots each point defined by

TSTEP

TMAX

and Y. The Window variables define the viewing window.

As a graph is plotted, the TI-80 updates X, Y, and T.

Note: Smart Graph applies to parametric graphs also (page 4-11).

By means of the

VARS WINDOW...

and

Y-VARS

menus, you

can:

Access functions by using the name of the component of the equation as a variable.

Select or deselect parametric equations from a program, using the

Store parametric equations.

Store values directly to Window variables.

FNON

and

commands (page 4-8).

FNOFF

Parametric Graphing 5-5

Exploring a Parametric Graph

As in function graphing, three tools are available for exploring a graph: the freemoving cursor, tracing, and zooming.

Free-Moving Cursor

Tracing a Parametric Graph

Zooming in on a Parametric Graph

The free-moving cursor works the same in parametric graphing as in function graphing (page 4-12).

or 9

puts the Trace cursor on the first selected

. You can then trace along the equation.

TMIN

Moves the cursor one

Moves the cursor five

TSTEP TSTEP

Changes to the previous or next equation.

at a time.

s at a time.

Pressing equation, at

2 6

The equation number shows in the upper right of the display.

For each value of

Cancels tracing.

, the calculator displays values for X and

The values for X, Y, and T are updated as you move the Trace cursor. If the cursor moves off the top or bottom of the screen, the coordinate values continue to change appropriately.

The Trace cursor remains in the same location if you leave

and return, unless Smart Graph replots the graph.

TRACE

QuickZoom is available in parametric graphing, but panning is not (page 4-13).

Pressing

works the same in parametric graphing as in

function graphing (page 4-15).

Parametric graphing uses the additional Window variables

TMIN, TMAX

, and

zooming unless you select

= 6.283185307 (2p), and

TMAX

. These variables are not affected by

TSTEP

ZSTANDARD

TSTEP

, where

= .1308996938996

TMIN

= 0,

(p/24).

5-6 Parametric Graphing

Chapter 6: Tables

This chapter describes how to use tables on the TI.80. A table evaluates the selected functions from the Y= list and displays each value for the independent variable along with the evaluated value for each corresponding dependent variable.

Chapter Contents

Getting Started: Roots of a Function Defining the Independent Variable Defining the Dependent Variable Displaying the Table

...............................

....................

.................

..................

6-2 6-3 6-4 6-5

Tables 6-1

Getting Started: Roots of a Function

Getting Started is a fast-paced introduction. Read the chapter for details.

Evaluate the function Y=X many sign changes are there, and where do they occur?

– 4X+3 at each integer between L10 and 10. How

1. If necessary, select Press 2

screen. Press · 10 to set

TBL=1

from the

FUNC

to display the

TBLMIN=L10

menu.

MODE

TABLE SETUP

. Leave

2. Press ( @ a | 4 @ « 3 to enter the function

Y1=X2 – 4X+3

3. Press 2

to display the table screen.

4. Press 8 repeatedly to view the changes in the value of

6-2 Tables

Texas Instruments TI-80 User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Table of Contents

Using this Guidebook Effectively

Glossary

Getting Started: Do This First!

TI-80 Keyboard

First Steps

TI-80 Menus

Entering a Calculation: Compound Interest

Continuing a Calculation

Defining a Function: Box with Lid

Defining a Table of Values

Zooming In on the Table

Changing the Viewing Window

Displaying and Tracing the Graph

Zooming In on the Graph

Chapter 1: Operating the TI-80

Turning the TI-80 On and Off

Setting the Display Contrast

The Display

Entering Expressions and Instructions

The Edit Keys

Setting Modes

TI-80 Modes

Variable Names

Storing and Recalling Variable Values

Last Entry

Last Answer

TI-80 Menus

The VARS and Y.VARS Menus

EOS (Equation Operating System)

Error Conditions

Chapter 2: Math, Angle, and Test Operations

Getting Started: Lottery Chances

Using the TI-80 Functions

Keyboard Math Operations

MATH MATH Operations

MATH NUM (Number) Operations

MATH PRB (Probability) Operations

ANGLE Operations

TEST (Relational) Operations

Chapter 3: Fractions

Getting Started: Working with Fractions

Setting Modes for Fraction Results

Entering and Using Fractions in Calculations

The FRACTION Menu

Chapter 4: Function Graphing

Getting Started: Graphing a Circle

Defining a Graph

Setting Graph Modes

Defining Functions in the Y= List

Evaluating Y= Functions in Expressions

Selecting Functions

Defining the Viewing Window

Displaying a Graph

Exploring a Graph with the Free-Moving Cursor

Exploring a Graph with TRACE

Exploring a Graph with ZOOM

Setting the Zoom Factors

Chapter 5: Parametric Graphing

Getting Started: Path of a Ball

Defining and Displaying a Parametric Graph

Exploring a Parametric Graph

Chapter 6: Tables

Getting Started: Roots of a Function