Texas instruments TI-82 Guidebook

TI-82

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.

Macintosh is a registered trademark of Apple Computer, Inc.

Important

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

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

US FCC Information Concerning Radio Frequency Interference

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

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

Reorient or relocate the receiving antenna.

•

Increase the separation between the equipment and receiver.

•

Connect the equipment into an outlet on a circuit different from that to

•

which the receiver is connected.

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

•

Caution:

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

Any changes or modifications to this equipment not expressly

This manual describes how to use the TI.82 Graphing Calculator. Getting Started gives a quick overview of its features. The first chapter gives general instructions on operating the TI.82. Other chapters describe its interactive features. The applications in Chapter 14 show how to use these features together.

Using this Guidebook Effectively Glossary

Getting Started: Do This First!

TI.82 Menus First Steps

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Entering a Calculation: Compound Interest Defining a Function: Box with Lid Defining a Table of Values Zooming In on the Table Changing the Viewing Displaying and Tracing the Graph Zooming In on the Graph Finding the Calculated Maximum Other Features

Chapter 1: Operating the TI.82

Turning the TI.82 On and Off Setting the Display Contrast The Display

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Entering Expressions and Instructions TI.82 Edit Keys Setting Modes TI.82 Modes

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Variable Names Storing and Recalling Variable Values

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Last Entry Last Answer

TI.82 Menus

VARS

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and

Y-VARS

EOSé (Equation Operating System) Error Conditions

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WINDOW

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viii

2 3 4 6 7

8 10 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 Keyboard Math Operations

MATH MATH MATH NUM MATH HYP MATH PRB ANGLE TEST TEST TEST LOGIC

Chapter 3: Function Graphing

Operations

(Number) Operations (Hyperbolic) Operations (Probability) Operations

Operations

(Relational) Operations

(Boolean) Operations

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

WINDOW FORMAT

Displaying a Graph

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WINDOW

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Exploring a Graph with the Free-Moving Cursor Exploring a Graph with Exploring a Graph with Using

ZOOM MEMORY

Setting

ZOOM FACTORS

Using

Chapter 4: Parametric Graphing

(Calculate) Operations

CALC

TRACE ZOOM

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

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List

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2-2 2-3 2-5

2-9 2-11 2-12 2-13 2-15 2-16

3-2

3-3

3-4

3-5

3-7

3-8 3-10 3-11 3-13 3-14 3-16 3-19 3-21 3-22

4-2

4-3

4-6

Chapter 5: Polar Graphing

Getting Started: Polar Rose Defining and Displaying a Polar Graph Exploring a Polar Graph

iv Introduction

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5-2

5-3

5-6

Chapter 6: Sequence Graphing

Getting Started: Forest and Trees Defining and Displaying a Sequence Graph Exploring a Sequence Graph

Chapter 7: Tables

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

Chapter 8: DRAW Operations

Getting Started: Shading a Graph

DRAW DRAW

Menu Drawing Lines Drawing Horizontal and Vertical Lines Drawing Tangent Lines Drawing Functions and Inverses Shading Areas on a Graph Drawing Circles Placing Text on a Graph Using

to Draw on a Graph

Pen

Drawing Points Drawing Pixels Storing and Recalling Graph Pictures Storing and Recalling Graph Databases Clearing a Drawing

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6-2 6-3 6-6

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

8-2 8-3 8-4 8-5 8-6 8-7 8-8

8-9 8-10 8-11 8-12 8-13 8-14 8-15 8-16

Chapter 9: Split Screen

Getting Started: Polynomial Coefficients Using Split Screen

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Introduction v

9-2

9-3

Chapter 10: Matrices

Getting Started: Systems of Linear Equations Defining a Matrix Viewing Matrix Elements Editing Matrix Elements About Matrices Matrix Math Functions

MATRIX MATH

Chapter 11: Lists

Getting Started: Generating Sequences About Lists

LIST OPS LIST MATH

Chapter 12: Statistics

Getting Started: Building Height and City Size Setting Up a Statistical Analysis Viewing List Elements Editing List Elements

STAT EDIT

Statistical Analysis Statistical Variables Types of Statistical Analysis Statistical Analysis in a Program Statistical Plotting Statistical Plotting in a Program

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Operations

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Operations

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

10-8 10-10 10-12

11-2

11-3

11-6

11-9

12-2

12-9 12-10 12-11 12-12 12-13 12-14 12-15 12-17 12-18 12-22

Chapter 13: Programming

Getting Started: Family of Curves About Programs Creating and Executing Programs Editing Programs

PRGM CTL PRGM I/O

Calling Other Programs

vi Introduction

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(Control) Instructions

(Input/Output) Instructions

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13-2

13-4

13-5

13-6

13-7 13-15 13-18

Chapter 14: Applications

Left-Brain, Right-Brain Test Results Speeding Tickets Buying a Car, Now or Later? Graphing Inequalities Solving a System of Nonlinear Equations Program: Sierpinski Triangle Cobweb Attractors Program: Guess the Coefficients The Unit Circle and Trigonometric Curves Ferris Wheel Problem Reservoir Problem Predator-Prey Model Fundamental Theorem of Calculus Finding the Area between Curves

Chapter 15: Memory Management

Checking Available Memory Deleting Items from Memory Resetting the TI.82

Chapter 16: Communication Link

Getting Started: Sending Variables TI.82

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LINK

Selecting Items to Send Transmitting Items Receiving Items Backing Up Memory

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14-2

14-4

14-5

14-6

14-7

14-8

14-9 14-10 14-11 14-12 14-14 14-16 14-18 14-20

15-2

15-3

15-4

16-2

16-3

16-4

16-6

16-7

16-8

Appendix A: Tables

Tables of Functions and Instructions Menu Map

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Table of System Variables

Appendix B: Reference Information

Battery Information In Case of Difficulty Accuracy Information Error Conditions

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Service and Support Information Warranty Information

Index

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Introduction vii

A-2 A-22 A-28

B-2

B-4

B-5

B-7 B-11 B-12

Using this Guidebook Effectively

The structure of the TI.82 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

The guidebook contains sections that 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 13, which describe specific functional areas of the TI.82. Each begins with a brief Getting Started introduction.

Chapter 14 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 15 describes memory management and Chapter 16 describes the communications link.

Page-Design Conventions

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 twopage 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.

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.

viii Introduction

Information-Mapping Conventions

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 must perform the steps sequentially.

“Bulleted” lists—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 examples identified with a



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, with problem-handling information.

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

) to highlight it—like this list.

Introduction ix

Glossary

v v

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

Expression

Function

Graph Database

Graph Picture

Home Screen

Instruction

List

Matrix

Menu Items Pixel

Variable

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

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 in graphing and

TABLE

editor used

A graph database is composed of the elements that define a graph: functions in the

list,

MODE

settings, and

WINDOW

settings. They may be saved as a unit in a graph database to recreate the graph later.

A picture is a saved image of a graph display, excluding cursor coordinates, axis labels, tick marks, and prompts. It may be superimposed on another graph.

The Home Screen is the primary screen of the TI.82, 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.

A list is a set of values that the TI.82 can use for activities such as graphing a family of curves, evaluating a function at multiple

alues, and entering statistical data.

A matrix is a two-dimensional array on which the TI.82 can perform operations.

Menu items are shown on full-screen menus.

A pixel (picture element) is a square dot on the TI.82 display. The TI.82 display is 96 pixels wide and 64 pixels high.

A variable is the name given to a location in memory in which a

alue, an expression, a list, a matrix, or another named item is

stored.

x Introduction

Getting Started: Do This First!

Getting Started contains two keystroke-by-keystroke examples, an interest rate problem and a volume problem, that introduce you to some principal operating and graphing features of the TI.82. You will learn to use the TI.82 much more quickly by completing both of these examples first.

Contents

TI.82 Menus First Steps Entering a Calculation: Compound Interest Defining a Function: Box with Lid Defining a Table of Values Zooming In on the Table Changing the Viewing Displaying and Tracing the Graph Zooming In on the Graph Finding the Calculated Maximum Other Features

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2 3 4 6 7

8 10 11 12 13 14

Getting Started 1

TI-82 Menus

To leave the keyboard uncluttered, the TI.82 uses full-screen menus to access many additional operations. The use of specific menus is described in the appropriate chapters.

Displaying a Menu

When you press a key that accesses a menu, such



as screen where you are working.

usually are returned to the screen where you were.

Moving from One Menu to Another

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

Use ~ or | 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:

Leaving without Making a Selection

To leave a menu without making a selection:

, that menu screen temporarily replaces the

fter you make a selection from a menu, you

menu key may access more than one menu. The

Use † and } to move the cursor to the item and then press

Press the number of the item.

QUIT

Press y

‘

Press

to return to the Home screen.

to return to the screen where you

were.

Select another screen or menu.

2 Getting Started

First Steps

Before beginning these sample problems, follow the steps on this page to reset the TI.82 to its factory settings. (Resetting the TI.82 erases all previously entered data.) This ensures that following the keystrokes in this section produces the illustrated actions.

1. Press É to turn the calculator on.

2. Press and release y and then press Ã. (Pressing y accesses the operation printed in blue to the left above the next key that you press.

The

3. Press 3 to select

The

is the

MEM

MEMORY

RESET MEMORY

2nd

menu is displayed.

Reset...

operation of Ã.)

menu is displayed.

4. Press 2 to select

. The calculator is reset.

Reset

5. After a reset, the display contrast is also reset. If the screen is very dark or blank, you need to adjust the display contrast. Press y and then press and hold † (to make the display lighter) or } (to make the display darker). You can

‘

press

to clear the display.

Getting Started 3

Entering a Calculation: Compound Interest

Using trial and error, determine when an amount invested at 6% annual compounded interest will double in value. The TI.82 displays up to 8 lines of 16 characters so you see an expression and its solution at the same time. You also can store values to variables, enter multiple instructions on one line, and recall previous entries.

1. Press

.06

Z (annual interest rate) to

store the interest rate.

2. Press y

to enter more than one instruction

on a line.

3. For the first guess, compute the amount available at the end of 10 years. Enter

(years).

4. Press y

, then enter the expression to

calculate the total amount available after years at Z interest just as you would write it. Use 1000 as the amount. Press

¤ ›

1000

¯ £ 1 Ã

The entire problem is shown in the first two lines of the display.

5. 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.

6. To save keystrokes, you can use

Last Entry

recall the last expression entered and then edit it for a new calculation. Press y, followed by

ENTRY

(above

The last calculated expression is shown on the next line of the display.

4 Getting Started

7. The next guess should be greater than 10

years. Make the next guess 12 years. Press to move the cursor over the to change 10 to 12. Press

, and then type

to evaluate the

}

expression.

8. To display answers in a format more

appropriate for calculations involving money, press z to display the

MODE

screen.

9. Press † ~ ~ ~ to position the cursor over the

2 and then press

. This changes the

display format to two fixed decimal places.

QUIT

10. Press y

(above z) to return to the

Home screen. The next guess should be less

than, but close to, 12 years. Press y

. Press

INS

(above {)

to evaluate the expression.

to change 12 to

}

11.9

ENTRY

11. If the amount above is to be divided among

seven people, how much will each person get? To divide the last calculated amount by seven, press ¥

, followed by

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

Ans

is displayed at

is a

Ans

variable that contains the last calculated answer.

Getting Started 5

Defining a Function: Box with Lid

Take a 200×250 mm. sheet of paper and cut X-by-X squares from two corners and X-by-125 mm. 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

olume 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

1. Press z † to

Float

2. Press y

to change the

MODE

back

Quit

‘

to return to the Home

screen and clear it.

3. Press

¿ ƒ

200

W y

to store the width and length of

250

the paper.

4. You define functions for tables and graphing on the

edit screen. Press o to access this

screen.

5. Enter the function for volume as

ƒ ¤ „ Í

„

. (

pressing

The

sign is highlighted to show that

„ ¤ £ ƒ

¹ 2

to define function

lets you enter X quickly, without

L ¥ 2 ¹

. Press

„

in terms of

selected.

XABXB

6 Getting Started

Defining a Table of Values

The table feature of the TI.82 provides numeric information about a function. Use a table of values from the previously defined function to estimate an answer to the problem.

TblSet

1. Press y

TABLE SETUP

2. Press

3. Press 10

Tbl=10

. Leave

(above

menu.

to accept

to define the table increment

Indpnt: Auto

so the table will be generated automatically.

4. Press y

TABLE

table.

Note that the maximum value displayed is at

. The maximum occurs between 30 and 50.

X=40

5. Press and hold † to scroll the table until the sign change appears. Note that the maximum length of sign of

6. Press y

for this problem occurs where the

(volume) becomes negative.

TblSet

. Note that to reflect the first line of the table you last displayed.

TblMin=0

(above

and

TblMin

) to display the

Depend: Auto

) to display the

has changed

Getting Started 7

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 set

2. Press y

TABLE

to set

Tbl

TblMin

. Press 1

3. Use † and } to scroll the table. Note that the maximum value displayed is occurs at

. The maximum occurs between

X=37

410256

36 and 38.

, which

8 Getting Started

4. Press y Press

5. Press y

TblSet

TABLE

. Press

to set

and use † and } to scroll the

Tbl

to set

table.

6. Press † and } to move the cursor. The maximum value of

36.8

410264

TblMin

7. Press ~ to display the value of precision,

410264.064

. This would be the

maximum volume of the box if you could cut your piece of paper at 1 mm. increments.

36.8

in full

Getting Started 9

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

The standard viewing and

Ymax

and

Xscl

marks on the

variables here.

WINDOW

variables define the

as shown.

Xmin, Xmax, Ymin

define the boundaries of the display.

define the distance between tick

Yscl

and Y axis.

2. Press † to move the cursor onto the line to define

Xmin

. Press 0

3. You can enter expressions to define values in the

WINDOW

4. Press

is stored in

100

as 10.

Xscl

5. Press 0 define the

editor. Press

. The expression is evaluated, and

. Press 10

Xmax

WINDOW

500000

variables.

200

100000

¥ 2.

to set

Ymax

Xmin

Xscl

Xmax

Yscl

Ymin

10 Getting Started

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

the viewing

The graph of

to graph the selected function in

WINDOW

Y1=(W–2X)(Là2–X)X

is shown in

the display.

2. Press ~ once to display the free-moving graph cursor just to the right of the center of the screen. The bottom line of the display shows the

and Y coordinate values for the position of the

graph cursor.

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

As you move the cursor,

and Y coordinate

values are updated continually with the cursor position.

4. Press

. The

function near the middle of the screen. 1 in

cursor appears on the

TRACE

the upper right corner of the display shows that the cursor is on trace along

. As you press | and ~, you

, one X dot at a time, evaluating

at each X.

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

Y1(X)

for the

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

Getting Started 11

Zooming 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.82 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

been adjusted in both the factors of 4, the values for

4. Press

to display the new

is displayed. It has

and Y directions by

factors.

ZOOM

WINDOW

settings.

12 Getting Started

Finding the Calculated Maximum

You can use a CALC operation to calculate a local maximum of a function.

CALC

1. Press y menu. Press 4 to select

The graph is displayed again, with a prompt for

Lower Bound?

2. Use | to trace along the curve to a point to the left of the maximum and then press

A triangle at the top of the screen indicates the selected bound. A new prompt is displayed for

Upper Bound?

3. Use ~ to trace along the curve to a point to the right of the maximum and then press

A triangle at the top of the screen indicates the selected bound. A new prompt is displayed for

Guess?

4. Use | to trace to a point near the maximum and

press bottom of the display.

Note how the values for the calculated maximum compared with the maximums found with the free-moving cursor, table.

to display the

maximum

CALCULATE

. The answer is displayed at the

, and the

TRACE

Getting Started 13

Other Features

Getting Started introduced you to basic calculator operation and the table and function graphing features of the TI.82. The remainder of this guidebook describes these features in more detail and also covers other capabilities of the TI.82.

Graphing

You can store, graph, and analyze up to ten functions (Chapter 3), up to six parametric functions (Chapter 4), and up to six polar functions (Chapter 5). You can use

Sequences

You can generate sequences and graph them over time or as web plots. (Chapter 6)

Tables

You can create function evaluation tables to analyze multiple functions simultaneously. (Chapter 7)

Matrices

You can enter and save up to five matrices and perform standard matrix operations on them. (Chapter 10)

Lists

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 and to graph a family of curves. (Chapter 11)

operations to annotate graphs (Chapter 8).

DRAW

Statistics

You can perform one-variable and two-variable list-based statistical analysis, including median-median line and regression analysis, and plot the data as histograms, points,

lines, or box-and-whisker plots. You can

x-y

define and save three statistical plot definitions. (Chapters 12).

Programming

You can enter and save programs that include extensive control and input/output instructions. (Chapter 13)

Split Screen

You can show simultaneously the graph screen and a related editor, such as the

screen, table, list editor, or Home screen. (Chapter 9)

14 Getting Started

Chapter 1: Operating the TI-82

This chapter describes the TI.82 and provides general information about its operation.

Chapter Contents

Turning the TI.82 On and Off

Setting the Display Contrast The Display

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Entering Expressions and Instructions TI.82 Edit Keys Setting Modes TI.82 Modes Variable Names

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Storing and Recalling Variable Values

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

Last Entry Last Answer

TI.82 Menus

VARS

EOS

Error Conditions

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and

Y.VARS

Equation Operating System

(

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)

1-2

1-3 1 1 1 1

13 1-14 1-16

17 1-19 1-20

Operating the TI.82 1-1

Turning the TI-82 On and Off

To turn the TI.82 on, press the É key. To turn it off, press and release y and then press M. After about five minutes without any activity, APDé (Automatic Power Down™) turns the TI.82 off automatically.

Turning the Calculator On

Press É to turn the TI.82 on.

If you pressed y the Home screen as it was when you last used it, and errors are cleared.

If APD turned the calculator off, the TI.82, including the display, cursor, and any error conditions, will be exactly as you left it.

Turning the Calculator Off

Press and release y and then press

Any error condition is cleared.

All settings and memory contents are retained by Constant Memoryé.

APD™ (Automatic Power Down™)

To prolong the life of the batteries, APD turns the TI.82 off automatically after several minutes without any activity. When you press É, the TI.82 will be exactly as you left it.

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

All settings and memory contents are retained by Constant Memory.

OFF

to turn the calculator off, the display shows

OFF

to turn the TI.82 off.

Batteries

The TI.82 uses four AAA alkaline batteries and has a user-replaceable backup lithium battery. To replace batteries without losing any information stored in memory, follow the directions on page B.2.

1-2 Operating the TI.82

Setting the Display Contrast

The brightness and contrast of the display depends on room lighting, battery freshness, viewing angle, and adjustment of the display contrast. The contrast setting is retained in memory when the TI.82 is turned off.

Adjusting the Display Contrast

You can adjust the display contrast to suit your viewing angle and lighting conditions at any time. As you change the contrast setting, the display contrast changes, and a number in the upper right corner indicates the current contrast setting between 0 (lightest) and 9 (darkest).

Note that there are 32 different contrast levels, so each number 0 through 9 represents more than one setting.

To adjust the contrast:

1. Press and release the y key.

2. Use one of two keys:

To increase the contrast, press and hold }.

To decrease the contrast, press and hold †.

Note: If you adjust the contrast setting to zero, the display may become completely blank. If this happens, press and release y and then press and hold } until the display reappears.

When to Replace Batteries

When the batteries are low, the display begins to dim (especially during calculations), and you must adjust the contrast to a higher setting. If you find it necessary to set the contrast to a setting of 8 or 9, you should replace the four AAA batteries soon.

Note: The display contrast may appear very dark after you change batteries. Press and release y and then press and hold † to lighten the display.

Operating the TI.82 1-3

The Display

The TI.82 displays both text and graphics. Graphics are described in Chapter 3. The TI.82 also can display a split screen, showing graphics and text simultaneously (Chapter 9).

Home Screen

The Home screen is the primary screen of the TI.82, where you enter instructions to be executed and expressions to be evaluated and see the answers.

Displaying Entries and Answers

When text is displayed, the TI.82 screen can have up to eight lines of up to 16 characters per line. If all lines of the display are filled, text “scrolls” off the top of the display. If an expression on the Home screen, the (Chapter 3), or the program editor (Chapter 13) is longer than one line, it wraps to the beginning of the next line. On numeric editors such as the

WINDOW

screen (Chapter 3), 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

editor

The

settings control the way expressions are interpreted and

MODE

answers are displayed (page 1.10).

If an answer, such as a list or matrix, is too long to display in its entirety, ellipsis marks (...) are shown at the left or right. Use ~ and | to scroll the answer and view all of it.

Returning to the Home Screen

Entry

Answer

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

1-4 Operating the TI.82

QUIT

Display Cursors

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

Cursor Appearance Meaning

Entry Solid blinking

rectangle

(insert) Blinking underline The next keystroke is inserted in front

INS

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

of the cursor location.

2nd ALPHA

Blinking # (arrow) The next keystroke is a

Blinking

The next keystroke is an alphabetic character.

“full” Checkerboard

rectangle

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

operation.

2nd

If you press to an underlined

If you press y or (such as the

or y during an insertion, the underline cursor changes

or # cursor.

on a screen on which there is no edit cursor

screen or a graph), # or A appears in the upper right

MODE

corner.

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

Busy Indicator

When the TI.82 is calculating or graphing, a moving vertical bar shows in the upper right of the display as a busy indicator. (When you pause a graph or a program, the busy indicator is a dotted bar.)

Operating the TI.82 1-5

Entering Expressions and Instructions

On the TI.82, you can enter expressions, which return a value, in most places where a value is required. You enter instructions, which initiate an action, on the Home screen or in the program editor (Chapter 13).

Expressions

An expression is a complete sequence of numbers, variables, functions, and their arguments that evaluate to a single answer. On the TI.82, you enter an

4 5

. You

expression in the same order that it normally is written. For example, is an expression.

Expressions can be used on the Home screen to calculate an answer. In most places where a value is required, expressions may be used to enter a value.

Entering an Expression

To create an expression, enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press regardless of the cursor location. The entire expression is evaluated according to EOS rules (page 1.20), and the answer displayed.

Most TI.82 functions and operations are symbols with several characters in them. You must enter the symbol from the keyboard or menu, not spell it out. For example, to calculate the log of 45, you must press « cannot type in the letters entry as implied multiplication of the variables

L O G

. (If you type

, the TI.82 interprets the

LOG

, and G.)

L, O

Calculate 3.76 ÷ (-7.9 + ‡5) + 2 log 45.



Multiple Entries on a Line

1-6 Operating the TI.82

¥ £ Ì

3.76

¤ Ã 2 «

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

Ã y

7.9 45

). They are all stored together in

‡

Last Entry

(page 1.14).

Entering a Number in Scientific Notation

1. Type the part of the number that precedes the exponent. This value can be an expression.

2. Press y

appears in the display.

3. If the exponent is negative, press Ì 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 or engineering notation. The display format is determined by the

Functions

A function returns a value. For example, ÷, -, +, ‡, and

settings (page 1.10) and the size of the number.

MODE

log

functions in the previous example. In general, the names of functions on the display begin with a lowercase letter. Some functions take more than one argument, which is indicated by a example,

Instructions

requires arguments,

min(

An instruction initiates an action. For example,

at the end of the name. For

(

min(5,8)

ClrDraw

is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. In general, the names of instructions begin with a capital letter. Some instructions require more than one argument, which is indicated by a arguments,

at the end of the name. For example,

(

Circle(0,0,5)

Circle(

were the

requires three

Interrupting a Calculation

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

To go to where the interruption occurred, select

To return to the Home screen, select

ERR:BREAK

screen is shown.

Quit

Goto

Operating the TI.82 1-7

TI-82 Edit Keys

}

†

y |

y ~

Í ‘ ¦

{

INS

A-LOCK

„

Moves the cursor within an expression. These keys repeat.

Moves the cursor between lines. These keys repeat.

Moves the cursor to beginning of expression.

Moves the cursor to end of expression.

Evaluates an expression or executes an instruction.

Deletes character at cursor. This key repeats.

Inserts characters at underline cursor. To end insertion, press

Next keystroke performs a left above a key). The cursor changes to an #. To cancel

Next keystroke is an right above the key). The cursor changes to an A. To cancel press

Sets character. The cursor changes to an A. To cancel press keyboard in

Allows you to enter an

Pol

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

On bottom line of an expression on the Home screen, † moves the cursor to end of expression.

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) expression or value where cursor is located; it does not store a zero.

INS

or a cursor-key.

operation (the blue operation to the

2nd

, press

character (the gray character to the

ALPHA

or a cursor-key.

ALPHA-LOCK

MODE

; each subsequent keystroke is an

ALPHA

ALPHA-LOCK

. Note that prompts for names automatically set the

ALPHA-LOCK

without pressing

Func

MODE

first.

, a T in

Par

MODE

, or a q in

ALPHA

1-8 Operating the TI.82

Setting Modes

Modes control how numbers and graphs are displayed and interpreted. MODE settings are retained by Constant Memoryé when the TI.82 is turned off. All numbers, including elements of matrices and lists, are displayed according to the current MODE settings.

Checking MODE Settings

Press z to display the highlighted. The specific pages.

settings. The current settings are

MODE

settings are described on the following

MODE

Normal Sci Eng Float 0123456789 Radian Degree Func Par Pol Seq Connected Dot Sequential Simul FullScreen Split

Changing MODE Settings

Numeric display format Number of decimal places Unit of angle measure Type of graphing Whether to connect graph points Whether to plot simultaneously Full or split screen

1. Use † or } to move the cursor to the line of the setting that you want

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

2. Use ~ or | to move the cursor to the setting that you want.

3. Press

Leaving the MODE Screen

To leave the

Setting a MODE from a Program

You can set a an instruction; for example, name from the interactive

screen:

MODE

Press the appropriate keys to go to another screen.

Press y

QUIT

MODE

‘

to return to the Home screen.

from a program by entering the name of the

Func

selection screen in the program editor

MODE

. From a blank line, select the

Float

(Chapter 13); the name is copied to the cursor location. The format for fixed decimal setting is

Fix

MODE

Operating the TI.82 1-9

TI-82 Modes

The TI.82 has seven MODE settings. Three are related to how numeric entries are interpreted or displayed and four are related to how graphs appear in the display. Modes are set on the MODE screen (page 1.9).

Normal, Sci, Eng

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

display format is the way in which we usually express numbers,

Normal

with digits to the left and right of the decimal, as in

(scientific) notation expresses numbers in two parts. The significant

Sci

12346.67

digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of

(engineering) notation is similar to scientific notation. However, the

Eng

, as in

1.234667E4

number may have one, two, or three digits before the decimal, and the power-of-10 exponent is a multiple of three, as in

12.34667E3

Note: If you select normal display format, but the answer cannot display in 10 digits or the absolute value is less than .001, the TI.82 changes to scientific notation for that answer only.

Float, Fix

Decimal settings affect only how an answer is displayed on the Home screen. They apply to all three notation display formats. You can enter a number in any format.

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

Float

decimal.

The fixed decimal setting displays the selected number of digits ( the right of the decimal. Place the cursor on the number of decimal digits you want and press

to 9) to

1-10 Operating the TI.82

Radian, Degree

Angle settings control how the TI.82 interprets angle values in trig functions and polar/rectangular conversions.

interprets the values as radians. Answers display in radians.

Radian

interprets the values as degrees. Answers display in degrees.

Degree

Func, Par, Pol, Seq

(function) graphing plots functions where Y is a function of

Func

(Chapter 3).

(parametric) graphing plots relations where X and Y are functions of

Par

(Chapter 4).

(polar) graphing plots functions where R is a function of q (Chapter 5).

Pol

(sequence) graphing plots sequences (Chapter 6).

Seq

Connected, Dot

Connected

draws a line between the points calculated for the selected

functions.

plots only the calculated points of the selected functions.

Dot

Sequential, Simul

Sequential

graphing evaluates and plots one function completely before the

next function is evaluated and plotted.

(simultaneous) graphing evaluates and plots all selected functions

Simul

for a single value of of

and then evaluates and plots them for the next value

FullScreen, Split

FullScreen Split

uses the entire screen to display a graph or edit screen.

screen displays the current graph on the upper portion of the screen

and the Home screen or an editor on the lower portion (Chapter 9).

Operating the TI.82 1-11

Variable Names

On the TI.82 you can enter and use several types of data, including real numbers, matrices, lists, functions, stat plots, graph databases, and graph pictures.

Variables and Defined Items

The TI.82 uses preassigned names for variables and other items saved in memory.

Variable type Names

, . . . ,

X6T/Y

, . . . ,

GDB6

Pic6

, and others

Real numbers

Matrices

Lists

Functions

Parametric equations

Polar functions

Sequence functions

Stat plots

Graph databases

Graph pictures

System variables

, . . . , Z,

A, B

ãAä, ãBä, ãCä, ãDä, ãEä

X1T/Y

V Plot1, Plot2, Plot3 GDB1, GDB2 Pic1, Pic2 Xmin, Xmax

Programs have user-defined names also and share memory with variables. Programs are entered and edited from the program editor (Chapter 13).

You can store to matrices (Chapter 10), lists (Chapter 11), system variables such as

(Chapter 3) or

Xmax

(Chapter 7), and all functions

TblMin

(Chapters 3, 4, 5, and 6) from the Home screen or from a program. You can store to matrices (Chapter 10), lists (Chapter 12), and functions (Chapter 3) from editors. You can store to a matrix element (Chapter 10) or a list element (Chapter 11). Graph databases and pictures are stored and recalled using instructions from the

menu (Chapter 8).

DRAW

1-12 Operating the TI.82

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

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 (which can be an expression).

2. Press ¿. The symbol

3. Press

, then the 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.

Displaying a Variable Value

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

RCL (Recall)

You can copy variable contents to the current cursor location. Press

RCL

, and then enter the name of the variable in one of the following ways:

Press

and then the letter of the variable.

Press y and the name of the list.



Press

Press y

Press

and select the name of the matrix.

Y.VARS



and select the name of the program (in the program editor

only).

You can edit the characters copied to the expression without affecting the value in memory.

Note: When an error (such as a variable with no assigned value) occurs on the name. To leave

line, the name is cleared automatically for you to enter the correct

RCL

without recalling a value, press

RCL

is copied to the cursor location.

and select the type and name of the function.

‘

Operating the TI.82 1-13

Last Entry

ENTRY

on the Home screen to evaluate an expression or execute

Last Entry

ENTRY

, it replaces what you have typed.

). They are all stored together in

R y ã:ä y

and edit it from the Home screen or any editor.

. On the Home screen or a numeric editor, the current

Last Entry

is copied to the line. The cursor is

Last Entry

is pressed, you can recall the previous entry

Last Entry

, use trial and error to find the radius of a circle

ãpä

(page 1.14).

Last Entry

When you press an instruction, the expression or instruction is stored in a storage area called Last Entry, which you can recall. When you turn the TI.82 off, Last Entry is retained in memory.

Using Last Entry

You can recall Press y line is cleared and the positioned at the end of the entry. In the program editor, the inserted at the cursor location. Because the TI.82 updates the storage area only when even if you have begun entering the next expression. However, when you recall



Multiple Entries on a Line

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

If the previous entry contained more than one expression or instruction, separated with a colon (page 1.7), 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 that covers 200 square centimeters. Use 8 as your first guess.



Í y

y | Í

Continue until the answer is as accurate as you want.

1-14 Operating the TI.82

.95

INS

Reexecuting the Previous Entry

To execute entry does not display again.



ƒ y Í Í

Accessing a Previous Entry

The TI.82 retains as many of the previous entries as is possible (up to a total of 128 bytes) in the entries by continuing to press y 128 bytes, it is retained for

Last Entry



Í y

Each time you press y press y displayed.

Ã 1 ¿

ã:ä

storage area.)

ENTRY

Last Entry

ƒ Í

A B C

ENTRY

after displaying the oldest item, the newest item is

press

Last Entry

on a blank line on the Home screen; the

storage area. You can access those

ENTRY

. (If a single entry is more than

Last Entry

ENTRY

, but it cannot be placed in the

, the current line is overwritten. If you

ENTRY

Operating the TI.82 1-15

Last Answer

When an expression is evaluated successfully from the Home screen or from a program, the TI.82 stores the answer to a variable, Ans (Last Answer). Ans may be a real number, a list, or a matrix. When you turn the TI.82 off, the value in Ans is retained in memory.

Using Ans in an Expression

You can use the variable

Press y When the expression is evaluated, the TI.82 uses the value of calculation.

Calculate the area of a garden plot 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

147

Continuing an Expression

You can use the value in without entering the value again or pressing y the Home screen, enter the function. The TI.82 “types” the variable name

Ans



9.9

ANS

and the variable name

4.2

¥ y

followed by the function.

ANS

to represent the last answer in most places.

Ans

is copied to the cursor location.

Ans

as the first entry in the next expression

Ans

ANS

. On the blank line on

in the

Storing Answers

To store an answer, store 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 and store in the



variable

y Í ¯ Í ¿ ƒ Í

1-16 Operating the TI.82

3.3

ãpä

to a variable before you evaluate another

Ans

TI-82 Menus

To leave the keyboard uncluttered, the TI.82 uses full-screen menus to access many operations. The use of specific menus is described in the appropriate chapters.

Moving from One Menu to Another

A menu key may access more than one menu. The names of the menus appear on the top line. The current menu is highlighted and the items in that menu are displayed.

Use ~ or | to move the cursor to 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 Menu items that end in

There are two methods of selecting from a menu.

Press the number of the item you want to select.

Use † and } to move the cursor to the item you want to select and then press

Leaving a Menu without Making a Selection

After you make a selection from a menu, you usually are returned to the screen where you were.

To leave a menu without making a selection, do any of the following:

Press y

‘

Press

Display a different menu by pressing the appropriate key, such as

Select another screen by pressing the appropriate key, such as

appears on the last line in place of the : (colon).

(ellipsis marks) access another menu.

...

QUIT

to return to the Home screen.

to return to the screen where you were.



Operating the TI.82 1-17

Calculate 6



1. Press 6. Press

2. To select

3. Press 27 and then press

‡

27.



to display the

‡

, you may either press 4 or press † † †

to evaluate the expression.

MATH

menu.

1-18 Operating the TI.82

VARS and Y-VARS Menus

Occasionally you may want to access the names of functions and system variables to use in an expression or to store to them directly. Use the VARS or Y.VARS menus to access the names of variables such as Xmin and functions

such Y

VARS Menu

Y-VARS Menu

The and databases and graph pictures such as such as

Press

menu accesses the names of

VARS

, the user-defined

Tstep

RegEQ



to display the

and

, and table variables such as

WINDOW

variables such as

ZOOM

VARS

GDB1

menu. Some of the items access more than

variables such as

ZXmin

and

, statistics variables

Pic2

TblMin

, graph

one menu of variable names.

VARS 1: Window 2: Zoom 3: GDB 4: Picture 5: Statistics 6: Table

The

…

Y-VARS

X/Y, T/ ZX/ZY, ZT/Z

GDB Pic

Table

U/V

variables

BOX, PTS

variables

, ZU variables

variables

…

Names of Names of Names of Names of

…

X/Y

Names of

, G, EQ,

menu accesses the names of functions and the instructions to

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

Press y

Y-VARS 1: Function 2: Parametric 3: Polar 4: Sequence 5: On/Off

…

Y-VARS

…

to display the

Displays names of Displays names of Displays names of Displays names of

Y-VARS

Y X r U

menu.

functions

Lets you select/deselect functions

functions

Xmin

Accessing a Name from a VARS or Y-VARS Menu

1. Press



or y

2. Select the type of name you want;

, use ~ or | to move to the menu you want, if necessary.

VARS Y-VARS

Y-VARS

. The

VARS

Picture...

, a single menu is displayed.

Y-VARS

Polar...

3. Select the name you want from the menu. It is copied to the cursor location.

Operating the TI.82 1-19

menu is displayed.

, for example.

EOS™ (Equation Operating System)

The Equation Operating System (EOSé) defines the order in which functions in expressions are entered and evaluated on the TI.82. EOS lets you enter numbers and functions in a simple, straightforward sequence.

Order of Evaluation

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 2, -1, !, ¡, r,

, and conversions.

Powers and roots, such as

Implied multiplication where the second argument is a number,

2^5

ariable name, list, or matrix or begins with an open parenthesis,

such as 4A,

Single-argument functions that precede the argument, such as

negation, ‡,

Implied multiplication where the second argument is a

3ãB

sin

(A+B)4

, or

log

, or

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

Permutations (

Multiplication and division.

Addition and subtraction.

Relational functions, such as > or .

Logic operator

Logic operators or and

) and combinations (

nPr

and

xor

‡

4(A+B)

2nDeriv(A2,A,6)

nCr

Asin 2

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, evaluated as

sin(fPart(ln 8))

sin fPart ln 8

Calculations within a pair of parentheses are evaluated first. Multiargument functions, such as

nDeriv(A2,A,6)

, are evaluated as they are encountered.

1-20 Operating the TI.82

Implied Multiplication

The TI.82 recognizes implied multiplication. For example, it understands

Parentheses

4 sin 46, 5(1+2)

, and

as implied multiplication.

(2…5)7

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

, and then multiplies the answer, 3, by 4.

1+2

, EOS first evaluates the portion inside

4(1+2)

You can omit any right (close) 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: If the name of a list or matrix is followed by an open parenthesis, it does not indicate implied multiplication. It is used to access specific elements in the list (Chapter 11) or matrix (Chapter 10).

Negation

To enter a negative number, use the negation function. Press Ì and then enter the number. On the TI.82, negation is in the fourth group in the EOS hierarchy. Functions in the first group, such as squaring, are evaluated before negation.

For example,

is a negative number (or 0);

square a negative number:

(M9)

. Use parentheses to

Note: Use the ¹ key for subtraction and the Ì key for negation. If you press ¹ to enter a negative number, as in indicate subtraction, as in

, it is interpreted as implied multiplication (

Ì 7, it is an error. If you press

¯ ¹ 7, or if you press Ì to

A…MB

Operating the TI.82 1-21

Error Conditions

The TI.82 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 displays immediately. Error codes and conditions are described in detail in Appendix B.

Diagnosing an Error

If the TI.82 detects an error, it displays the error screen.

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

DOMAIN

. Additional information about each error message is in Appendix

SYNTAX

If you select

, the cursor is displayed at the location where the

Goto

error was detected.

Note: If a syntax error was detected in the contents of a during program execution, this option returns the user to the not the program.

If you select

or press y

Quit

QUIT

‘

, you return to the Home

screen.

Correcting an Error

1. Note the type of the error.

2. Select

, if that option is available, and look at the expression for

Goto

syntax errors, especially at and in front of 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.

function

editor,

1-22 Operating the TI.82

Chapter 2: Math, Angle, and Test Operations

This chapter describes math, angle, and relational operations that are available on the TI.82. The most commonly used functions are accessed from the keyboard; others are accessed through full-screen menus.

Chapter Contents

Getting Started: Lottery Chances Keyboard Math Operations

MATH MATH MATH NUM MATH HYP MATH PRB

Operations

ANGLE TEST TEST TEST LOGIC

Operations

(Number) Operations (Hyperbolic) Operations (Probability) Operations

(Relational) Operations

(Boolean) Operations

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

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

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

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

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

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

2-2 2-3 2-5

2-9 2-11 2-12 2-13 2-15 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 6 numbers will be drawn out of 49. To win, you must pick all 6 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 number of items. Press

MATH PRB

nCr

menu. Press 3 or † †

. Press 6 to enter the number of items

selected.

2. Press

to evaluate the expression. This is the total number of possible combinations of 6 numbers drawn from a set of 49 numbers. With one ticket, you have one chance in 13,983,816 of winning.

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

¥ y

expressed in scientific notation on the TI.82 because it is so small. The decimal equivalent is

0.00000007151123842.

4. To calculate the probability of winning with five tickets, press ¯ 5

small to display in fixed notation. The decimal equivalent is 0.0000003575561921.

to enter the total

 |

to display the

to select

ANS

. The answer is

. Again, the answer is too

2-2 Math, Angle, and Test Operations

Keyboard Math Operations

The most commonly used math functions are on the keyboard.

Using Lists with Functions

Functions that are valid for lists return a list calculated on an element-byelement basis. If two lists are used in the same expression, they must be the same length.

+ (Add), – (Subtract), … (Multiply), à (Divide)

(addition Ã), – (subtraction ¹), … (multiplication ¯), and à (division ¥)

may be used with numbers, expressions, lists, or matrices (Chapter 10).

valueA

Trig Functions

The trigonometric functions may be used with numbers, expressions, or lists. They are interpreted according to the current setting. For example,

Degree sin sin

arctangent).

sin

valueB, valueA–valueB, valueA…valueB, valueAàvalueB

Radian/Degree

value

MODE

cos

, and

cos

sin 30

it returns .5.

value

tan

value

tan

are the inverse trig functions (arcsine, arccosine, and

value

tan

Radian

MODE

returns

.9880316241

MODE

; in

(Power), 2 (Square), ‡ (Square Root)

‡

(power ›), 2 (squared ¡), and ‡ (square root y

) may be used with

numbers, expressions, lists, or matrices (Chapter 10).

value

power, value

value

‡

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

(Inverse)

(inverse —) may be used with numbers, expressions, lists, or matrices (Chapter 10).The multiplicative inverse is the equivalent of the reciprocal, 1àx.

value

Math, Angle, and Test Operations 2-3

log, 10^, ln

), and

returns the value of the

e^1

(natural log

(logarithm «),

log

) may be used with a number, expression, or list.

log

e^ e^

10^

value

power

(exponential y returns the constant e raised to a power.

(power of ten y

10^

value

) may be used with a number, expression, or list.

constant e.

power

(Negation)

(negation Ì) returns the negative of a number, expression, list, or matrix (Chapter 10). The narrow negation symbol ( the subtraction or minus ¹ (

value

EOS rules (Chapter 1) determine when negation is evaluated. For example,

returns a negative number (squaring is evaluated before negation

according to EOS rules). Use parentheses to square a negated number,

(MA)

) distinguishes negation from

abs

(absolute value) returns the absolute value of a number, expression,

abs

list, or matrix (Chapter 10).

abs

value

(Pi)

Pi is stored as a constant in the TI.82. Press y

to copy the symbol the cursor location. The number 3.1415926535898 is used internally in calculations.

2-4 Math, Angle, and Test Operations

MATH MATH Operations

To display the MATH MATH menu, press . When you select an item from the menu, 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

MATH NUM HYP PRB 1:8Frac 2:8Dec

‡

5: 6: fMin( 7: fMax( 8: nDeriv( 9: fnInt( 0: solve(

Frac

(display as fraction) displays an answer as the rational equivalent.

Frac

The answer may be a number, expression, list, or matrix. If it cannot be simplified or the denominator is more than three digits, the decimal equivalent is returned.

expression

Frac

Display answer as fraction Display answer as decimal Cube Cube root

root Minimum of a function Maximum of a function Numerical derivative Function integral Solution (root) of a function

is valid only at the end of an expression.

Frac

Dec

(display as decimal) displays an answer in decimal form.

Dec

valid only at the end of an expression.

expression

Dec

Math, Angle, and Test Operations 2-5

(Cube)

(cube,

MATH MATH

item 3) returns the cube of a number, expression, list,

or square matrix (Chapter 10).

value

‡

(Cube Root)

‡

(cube root,

MATH MATH

item 4) returns the cube root of a number,

expression, or list.

value

‡

(Root)

‡

(root,

MATH MATH

item 5) returns the

expression, or list.

root

value

‡

fMin(, fMax(

(function minimum,

fMin(

maximum,

MATH MATH

maximum value of

lower

and

tolerance

upper

and

fMax(

values for

are not valid in

(optional; if not specified, 1

MATH MATH

item 7) return the value at which the minimum or

expression

with respect to

variable. lower

expression

item 6) and

must be less than

. The accuracy is controlled by

5 is used). If there is no finite minimum or maximum in the interval, usually (depending on an error occurs.

expression,variable,lower,upper

fMin(

expression,variable,lower,upper,tolerance

fMin(

)

real root of a number,

(function

fMax(

variable

occurs, between

upper

expression

)

fMin(

)

2-6 Math, Angle, and Test Operations

nDeriv(

(numerical derivative,

nDeriv(

derivative of

expression

MATH MATH

with respect to

item 8) returns an approximate

variable

, given the to calculate the derivative, and H (optional; if none is specified, 1 used).

expression,variable,value

nDeriv(

expression,variable,value,H

nDeriv(

uses the symmetric difference quotient method, which

nDeriv(

)

approximates the numerical derivative value as the slope of the secant line through the points:

value–H, expression(value–H

(

value+H,expression(value+H

(

)) and ))

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

value

at which

3 is

can be used once in

nDeriv(

expression

. Because of the method,

can return a false derivative value at a nondifferentiable point.

fnInt(

(function integral,

fnInt(

MATH MATH

(Gauss-Kronrod method) of

lower

limit,

upper

limit, and a

expression

item 9) returns the numerical integral

with respect to

tolerance

(optional; if none is specified, 1

is used).

expression,variable,lower,upper

fnInt(

expression,variable,lower,upper,tolerance

fnInt(

is not valid in

fnInt(

expression

)

Math, Angle, and Test Operations 2-7

nDeriv(

variable

)

, given

solve(

(

solve(

variable

MATH MATH

, given an initial

item 0) returns a solution (root) of

guess

, a

lower

which a solution is sought (optional, if not specified,

upper

solve( solve(

expression

not be updated. stored to every variable in is evaluated.

Controlling the Solution for solve(

99).

expression,variable,guess

)

expression,variable,guess,{lower,upper

is assumed equal to zero. The value of

guess

may be a value or a list of two values. Values must be

expression

lower

and

upper

are entered in list format.

bound, and an

})

, except

variable

expression

upper

lower

variable

, before

The TI.82 solves equations through an iterative process. To control that process, you should provide a close bound of the solution and at least one initial guess (which must be within the bounds). This will help to:

Find a solution.

Define which solution you want for equations with multiple solutions.

Find the solution more quickly.

for

bound within

99 and

=.1

in memory will

expression

2-8 Math, Angle, and Test Operations

MATH NUM (Number) Operations

To display the MATH NUM menu, press menu, 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

MATH NUM HYP PRB

round(

iPart

1: round( 2: iPart 3: fPart 4: int 5: min( 6: max(

returns a number, expression, list, or matrix rounded to

round(

#decimals

(9). If

value,#decimals

round(

value

round(

iPart

)

(integer part) returns the integer part or parts of a number,

Round Integer part Fractional part Greatest integer Minimum value Maximum value

is omitted,

)

 ~

. When you select an item from the

value

is rounded to 10 digits.

#decimals

expression, list, or matrix (Chapter 10).

value

iPart

fPart

(fractional part) returns the fractional part or parts of a number,

fPart

expression, list, or matrix (Chapter 10).

value

fPart

Math, Angle, and Test Operations 2-9

int

(greatest integer) returns the largest integer less than or equal to a

int

number, expression, list, or matrix. The value is the same as nonnegative numbers and negative integers, but one integer less than for negative noninteger numbers.

value

int

min(, max(

(minimum value) returns the smaller of

min(

valueA

valueB

smallest element in a list. If two lists are compared, it returns a list of the smaller of each pair of elements.

(maximum value) returns the larger of

max(

valueA

valueB

element in a list. If two lists are compared, it returns a list of the larger of each pair of elements.

valueA,valueB

min(

list

min(

listA,listB

min(

)

valueA,valueB

max(

list

max(

listA,listB

max(

)

for

iPart

or the

or the largest

Note: The as the

min(

and

max(

functions on the

max(

functions on the

2-10 Math, Angle, and Test Operations

MATH NUM

LIST MATH

menu are the same

menu.

MATH HYP (Hyperbolic) Operations

To display the MATH HYP menu, press

 ~ ~

. When you select an item from the menu, 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 HYP Menu

MATH NUM HYP PRB 1: sinh 2: cosh 3: tanh 4: sinh 5: cosh 6: tanh

–1

Hyperbolic sine Hyperbolic cosine Hyperbolic tangent Hyperbolic arcsine Hyperbolic arccosine Hyperbolic arctangent

sinh, cosh, tanh

sinh, cosh

value

sinh

sinh–1, cosh–1, tanh

–1

sinh

cosh

, and

are the hyperbolic functions. They are valid for lists.

tanh

–1

, and

–1

are the hyperbolic arcsine, hyperbolic arccosine,

tanh

and hyperbolic arctangent functions, respectively. They are valid for lists.

–1

value

sinh

Math, Angle, and Test Operations 2-11

MATH PRB (Probability) Operations

To display the MATH PRB menu, press menu, 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

MATH NUM HYP PRB

rand

1: rand 2: nPr 3: nCr 4: !

(random number) generates and returns a random number greater

rand

Random number generator Number of permutations Number of combinations Factorial

 |

. When you select an item from the

than 0 and less than 1. A random number is generated from a seed value. To control a random number sequence, first store an integer seed value in

rand

you reset the TI.82,

nPr

taken

items

nCr

items

. If you store 0 to

(number of permutations) returns the number of permutations of

number

at a time.

number

nPr

(number of combinations) returns the number of combinations of

number

taken

, the TI.82 uses the factory-set seed value. When

rand

is set to the factory seed.

rand

items

at a time.

and

items

number

must be nonnegative integers.

number

and

must be nonnegative

items

integers.

nCr

number

items

! (Factorial)

(factorial) returns the factorial of a positive integer between 0 and 69.

value

2-12 Math, Angle, and Test Operations

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 entries are interpreted according to the Radian/Degree MODE setting.

ANGLE Menu

ANGLE

1: 2: '

3: 4:8DMS 5: R8Pr( 6: R8Pq( 7: P8Rx( 8: P8Ry(

Degree function DMS entry notation Radian function Display as degree/minute/second Returns R, given X and Returns q, given X and Returns X, given R and Returns Y, given R and

;

. The ANGLE menu displays angle

q q

Note: Do not enter DMS numbers as

54¡32'30"

interpreted as implied multiplication of 54

on the TI.82.

and 32', and " is a quote mark

used to enter text.

(Degree)

(degree) lets you designate

setting.

MODE

angle

' (DMS Entry Notation)

(DMS entry notation) lets you enter degrees, minutes, and seconds in DMS

angle

may be a list.

angle

as degree, regardless of the current angle

format.

degrees

For example, enter the

minutes'seconds

setting must be

MODE

for 30 degrees, 1 minute, 23 seconds. Note that

30'1'23'

(or you must use the

Degree

for the TI.82 to interpret the argument as degrees, minutes, and seconds.

Degree

MODE

Radian

MODE

(Radians)

(radian) lets you designate

MODE

angle

setting.

angle

may be a list.

angle

as radian, regardless of the current angle

Degree

54¡32'

function)

Math, Angle, and Test Operations 2-13

DMS

(display as degree/minute/second) displays

DMS

minute, second format. The interpret

answer

as degrees, minutes, and seconds.

the end of a line.

answer

DMS

R8Pr(, R8Pq(, P8Rx(, P8Ry(

converts rectangular to polar and returns R, and

R8Pr(

rectangular to polar and returns values.

R8Pr(X,Y)

X,Y

R8Pq(

)

answer

in degree,

setting must be

MODE

, given X and Y rectangular coordinate

Degree

DMS

R8Pq(

for the TI.82 to

is valid only at

converts

converts polar to rectangular and returns X, and

P8Rx(

polar to rectangular and returns

P8Rx(R,q)

P8Ry(

,q)

, given R and q polar coordinate values.

2-14 Math, Angle, and Test Operations

P8Ry(

converts

TEST TEST (Relational) Operations

To display the TEST TEST menu, press 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 TEST Menu

TEST LOGIC 1: =

2: 3: >

‚

4: 5: <



True if:

Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to

. When you select from the menu,

=, ƒ, >, ‚, <,



Relational operators compare true or

if the test is false.

valueA

and

valueB

and return 1 if the test is

can be numbers, expressions, lists, or matrices (Chapter 10), but they must match in type and dimension. 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

Using Tests

valueB

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

The expression

2+2=2+3

returns 0. The TI.82 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.82 first performs the

relational test because it is in parentheses, and then it adds 2, 1, and 3.

Math, Angle, and Test Operations 2-15

TEST LOGIC (Boolean) Operations

To display the TEST LOGIC menu, press menu, the name is copied to the cursor location.

TEST LOGIC Menu

TEST LOGIC 1: and 2: or 3: xor 4: not

Boolean Operators

True if:

Both values are nonzero (true) At least one value is nonzero (true) Only one value is zero (false) The value is zero (true)

Boolean operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values. Values are interpreted as zero (false) or nonzero (true).

and, or, xor

, and

and, or

if the expression is false, according to the table below.

(exclusive or) return a value of 1 if a expression is true or

xor

can be expressions.

~. When you select from the

valueA

and

valueB

valueA valueA valueA

valueA

valueB

and

valueB

xor

valueB

0 0 returns 0 1 1

0 returns 1 1 0

0 returns 0 1 1

and or xor

0 0 returns 0 0 0

not

returns 1 if

not

value

not

Using Boolean Operations

value

(which can be an expression) is 0.

Boolean logic is often used with relational tests. In a program, the following instructions store

into C:

2-16 Math, Angle, and Test Operations

Chapter 3: Function Graphing

This chapter describes function graphing on the TI.82 in detail. It also lays the foundation for using the other graphing features of the TI.82.

Chapter Contents

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

WINDOW FORMAT

Displaying a Graph

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

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

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

WINDOW

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

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

Exploring a Graph with the Free-Moving Cursor Exploring a Graph with Exploring a Graph with Using

ZOOM MEMORY

Setting

ZOOM FACTORS

Using

(Calculate) Operations

CALC

TRACE ZOOM

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

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

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

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

List

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

........

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

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

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

3-10 3-11 3-13 3-14 3-16 3-19 3-20 3-21

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

Function Graphing 3-1

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 ZOOM Square to adjust the display to make the functions appear as a circle.

1. In

Func

, press o to display the Y= edit

MODE

screen. Press y

‡

„ ¡ ¤ Í

100

to enter the expression to define the top half of the circle,

Y1=‡(100–X2)

The bottom half of the circle is defined by

Y2=M‡(100–X2)

. However, on the TI.82 you can

define one function in terms of another, so to

define the

(to select

2. Press

, press Ì y

Y2=MY

variables menu) 1 (to select

and then select

quick way to reset the

Y.VARS

ZStandard

WINDOW

(to display

Function...) 1

. This is a

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 effect of variables, press values for

Xmin, Xmax, Ymin

ZSquare

on the

WINDOW

and notice the new

, and

Ymax

3-2 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 WINDOW FORMAT. Once you have defined a graph, you can plot, display, and explore it.

Steps in Defining a Graph

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

1. Set the

2. Enter or edit a function in the Y= list.

3. Select the Y= function you want to graph.

4. Define the viewing

5. Set the

6. Deselect stat plots, if appropriate (Chapter 12.)

Exploring a Graph

Once you have defined a graph, you can display it and then use several tools of the TI.82 to explore the behavior of the function or functions. These tools are described later in this chapter.

Saving a Graph

You can store the elements that define the current graph in one of six graph databases (Chapter 8). Later, you can recall that database to recreate the current graph.

You can store a picture of the current graph display in one of six graph pictures (Chapter 8). Later, you can superimpose that picture on the current graph.

MODE

WINDOW FORMAT

Func

WINDOW

graphing.

variables.

Function Graphing 3-3

Setting Graph Modes

Pressing z displays the current MODE settings (Chapter 1). The graphing MODE in function graphing must be Func.

Checking and Changing Graphing Modes

Press z to display the highlighted.

The TI.82 has four graphing modes.

¦ ¦ ¦ ¦

(function graphing)

Func

(parametric graphing)

Par

(polar graphing)

Pol

(sequence graphing)

Seq

To graph functions, you must select of graphing on the TI.82 are described in this chapter. Differences in parametric graphing (Chapter 4), polar graphing (Chapter 5), and sequence graphing (Chapter 6) are described in those chapters.

Radian Connected Sequential

Degree

MODE

affects how the selected functions are plotted.

Dot

affects how functions are plotted if you have more

Simul

than one function selected.

Setting Modes from a Program

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

Begin on a blank line in the program editor. Press z to display the interactive on the

MODE

is copied to the cursor location.

MODE

selection screen. Use †, }, ~, and | to place the cursor

MODE

that you want to select, and press

settings. The current settings are

MODE

(function graphing). The basics

Func

may affect how some functions are interpreted.

. The name of the

3-4 Function Graphing

Defining Functions in the Y= List

Pressing o accesses the Y= edit screen, where you enter the functions to graph. You can store up to ten 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

Press o to display the Y= edit screen. In the example below, the functions are defined.

Defining a New Function

To define a new function, enter an expression on the Y= edit screen.

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

to erase a previously entered function.

‘

2. Enter the expression to define the function.

You may use functions and variables (including matrices and lists) 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

, for the

variable. (

defines the independent variable as X.)

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

list as you enter it.

3. When you complete the expression, press

to move to the

beginning of the next function.

Func

MODE

and

„

Function Graphing 3-5

Editing a Function

1. Move the cursor to the function in the Y= list you want to change.

2. Make the changes. You can press

‘

to erase the expression and

then enter a new expression.

The expression is stored as one of the ten user-defined functions in the list as you enter it.

Clearing a Function

To clear or erase a function on the Y= edit screen, position the cursor anywhere on the function, and then press

Defining Functions from the Home Screen or a Program

1. Begin on a blank line. Press

press

again.

‘

, enter the expression, and then

2. Press ¿.

3. Press y

Y.VARS

, select

Function...

, and then select the name of the

function, which is copied to the cursor location.

4. Press

expression

to complete the instruction.

"!Y

When the instruction is executed, the TI.82 stores the expression to the list, selects the function, and displays the message

Evaluating Y= Functions in Expressions

Done

You can the calculate the value of a Y= function at a specified value of X. For example, if

Y1=.2X3–2X+6

3-6 Function Graphing

Selecting Functions

Only functions that are selected are graphed. Up to ten functions may be selected at one time.

Turning a Function “On” or “Off”

You select and deselect (“turn on” and “turn off”) functions on the Y= edit screen. The = sign on a selected function is highlighted. To change the selection status of a function:

1. If the

2. Move the cursor to the function whose status you want to change.

3. Use | to place the cursor over the = sign of the function.

4. Press

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

Leaving the Y= Edit Screen

To leave the Y= edit screen:

Select another screen by pressing the appropriate key, such as or

Press y

Selecting Functions from the Home Screen or a Program

1. Begin on a blank line. Press y

ON/OFF

2. Select the instruction you want, cursor location.

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

When the instruction is executed, the status of each function in the current graph mode is set appropriately and

FnOn FnOff FnOn FnOff

For example, in

list and then turns on

edit screen is not displayed, press o to display the functions.

to change the status.

QUIT

to return to the Home screen.

Y.VARS

and select

On/Off...

menu is displayed.

function1,function2

Func

MODE

. . .

FnOff:FnOn 1,3

and

FnOn

Done

is displayed.

. It is copied to the

FnOff

turns off all functions in the

. The

Function Graphing 3-7

Defining the Viewing

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

TI-82 Viewing WINDOW

The viewing defined by is defined by

WINDOW

Xmin, Xmax, Ymin

Xscl

of the TI.82 is the portion of the coordinate plane

for the X axis and

Ymax

, and

. The distance between tick marks

Ymax

for the Y axis.

Yscl

Xmin

Checking the Viewing WINDOW

Press

Xscl

Xmax

Yscl

Ymin

to display the current

WINDOW

variable values. The values

shown here are the standard values.

Changing a WINDOW Variable Value

1. Press † 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

Í, †

, or }. If you entered an expression, it is evaluated. The

new value is stored.

must be less than

Xmin

get an error message when you press

Xscl=0

Yscl=0

Xmax

and

must be less than

Ymin

. To turn off the tick marks, set

Ymax

, or you will

3-8 Function Graphing

Leaving the WINDOW Edit Screen

To leave the

Select another screen by pressing the appropriate key, such as

WINDOW

edit screen:

or o.

Press y

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

QUIT

to return to the Home screen.

Begin on a blank line.

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

2. Press ¿.

3. Press

4. Select

5. Select the



to display the

Window...

WINDOW

menu.

VARS

to display the

WINDOW

variables.

variable to which you want to store. The name of

the variable is copied to the cursor location where you are editing.

6. Press

to complete the instruction.

When the instruction is executed, the TI.82 stores the value in the

WINDOW

Note: You can use a

variable.

WINDOW

variable in an expression by performing

steps 3, 4, and 5.

X and @Y

The variables

and

define the distance between the centers of two

adjoining pixels on a graph (graphing accuracy).

(

–

Xmax

)(

Xmin

Ymax

–

Ymin

)

94 62

and

VARS Window

Ymax

are not on the

menu.

and

WINDOW

when a graph is displayed.

You can store values directly to are calculated from

Xmin

screen; they are accessible through the

are calculated from

, and

and

Ymin

, in which case

immediately.

Xmin, Xmax, Ymin

Xmax

Function Graphing 3-9

and

, and

Ymax

Setting WINDOW FORMAT

WINDOW FORMAT determines how a graph appears on the display. WINDOW FORMAT settings apply to all graphing modes.

Checking WINDOW FORMAT

To display the

WINDOW FORMAT

screen, press

settings are highlighted.

WINDOW FORMAT RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn

Changing WINDOW FORMAT

Sets rectangular or polar cursor. Sets cursor coordinates on or off. Sets grid off or on. Sets axes on or off. Sets axes label off or on.

1. Move the cursor to the row of the setting you want to change. The setting the cursor is on blinks.

2. Move the cursor to the setting you want and press

RectGC, PolarGC

The cursor coordinate setting determines if the cursor location is displayed (if

CoordOn

) as rectangular coordinates X and Y or polar coordinates and q. It also determines which variables are updated. In (rectangular graphing coordinates)

FORMAT

the free-moving cursor, or tracing updates and displays (polar graphing coordinates)

FORMAT

, X, Y, R, and q are updated, and

and q are displayed.

p ~

. The current

RectGC

, plotting the graph, moving

and Y. In

PolarGC

CoordOn, CoordOff

CoordOn

(coordinates on) displays the function number in the upper-right corner and the cursor coordinates at the bottom of the graph. (coordinate off) does not display the function number or the coordinates for the free-moving cursor or during

GridOff, GridOn

Grid points correspond to the axis tick marks. points.

AxesOn, AxesOff

AxesOn

does display the grid points.

GridOn

displays the axes.

AxesOff

does not display the axes. It overrides

TRACE

does not display grid

GridOff

the Axis Label setting.

LabelOff, LabelOn

LabelOn

and

LabelOff

determine whether to display a label for the axes (

and Y).

3-10 Function Graphing

CoordOff

Displaying a Graph

Pressing MODE settings apply, and the current values of the WINDOW variables define the viewing WINDOW.

Displaying a New Graph

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

Press

to display the graph of the selected function or functions.

(Some operations, such as

TRACE

and the

ZOOM CALC

operations, display

the graph automatically.) As a graph is plotted, the busy indicator is on and

and Y are updated.

Pausing a Graph

Note: While a graph is being plotted, you can:

Smart Graph

When you press

Press

Press É to stop graphing, then press

to pause graphing, then press

, Smart Graph displays the graph screen

to resume plotting.

to start over.

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

If you have not changed any of the following since the graph was last displayed, Smart Graph displays the graph immediately. If you have changed one or more of these, pressing

replots the graph based on

the new values.

Changed a

Changed a function.

Selected or deselected a function.

Changed the value of a variable in a selected function.

Changed a

Cleared drawings by selecting

Changed a

setting that affects graphs.

MODE

WINDOW

STAT PLOT

variable or a

definition (Chapter 12).

FORMAT

ClrDraw

setting.

(Chapter 8).

Function Graphing 3-11

Graphing a Family of Curves

If you enter a list (Chapter 11) as an element in an expression, the TI.82 plots the function for each value in the list, graphing a family of curves. (In

, it graphs all functions for the first element, and so on.)

Simul {2,4,6}sin X

graphs three functions:

2 sin X, 4 sin X

, and

6 sin X

{2,4,6}sin {1,2,3}X

graphs

2 sin X, 4 sin 2X

, and

6 sin 3X

3-12 Function Graphing

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

You can use |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. As soon as you press |, ~, }, or †, the cursor moves from the center of the viewing window.

As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen (if Coordinate values generally appear in normal floating-decimal format. The numeric display settings on the

screen do not affect coordinate

MODE

display.

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

. When you press |, ~, }, or †, the cursor moves from same

position.

Graphing Accuracy

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 3.14).

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

Xmax

(and

Ymin

and

) get closer together (after a

Ymax

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

CoordOn

Zoom In

‘

Xmin

, for

Free-moving cursor “on” the curve

)

Function Graphing 3-13

Exploring a Graph with TRACE

TRACE moves the cursor from one plotted point to the next along a function, while displaying the cursor coordinates at the bottom of the screen.

Beginning a Trace

Press displays it. The cursor is on the first selected function in the middle upper right of the display.

Moving along a Function

and | move the cursor along the function. Each press moves the cursor from one plotted point to the next. y ~ and y | move the cursor five plotted points at a time. The

Y=Yn(X)

to begin a trace. If the graph is not displayed already, the TI.82

list at the

value on the screen. The number of the function shows at the

value is calculated from the X value; that is,

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

)

cursor on the curve.

TRACE

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.

Panning to the Left or Right

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

Xmin

and

to correspond to the new viewing window.

QuickZoom

While tracing, you can press

to adjust the viewing the cursor location becomes the center of the new viewing if the cursor is above or below the display. This allows “panning” up and down. After QuickZoom, the cursor remains in

TRACE

are updated

Xmax

WINDOW

so that

, even

3-14 Function Graphing

Moving from Function to Function

To trace another selected function on the graph, use † or } to move the cursor to that function. 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. The cursor moves to the new function at the same value. The function number in the upper right corner of the display changes.

Leaving TRACE

To leave

Select another screen by pressing the appropriate key, such as

Press y

The

TRACE

QUIT

to return to the Home screen.

cursor remains in the same location if you leave

return, if Smart Graph has not caused the graph to be replotted.

Using TRACE in a Program

On a blank line in the program editor, press

. The instruction copied to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the

TRACE

first selected function. As you trace, the cursor coordinate values are updated. When you are done tracing functions, press

program execution.

and

TRACE

Trace

cursor on the

to resume

Function Graphing 3-15

Exploring a Graph with ZOOM

Pressing of the graph quickly in a variety of ways. All of the ZOOM commands are accessible from programs.

ZOOM Menu

ZBox

accesses a menu that allows you to adjust the viewing WINDOW

ZOOM MEMORY 1: ZBox 2: Zoom In 3: Zoom Out 4: ZDecimal 5: ZSquare 6: ZStandard 7: ZTrig 8: ZInteger 9: ZoomStat

lets you use the cursor to select opposite corners of a box to define a

ZBox

new viewing

1. Select

the screen indicates that you are using a

Draws box to define viewing 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 Sets built-in trig

WINDOW

Sets integer values on X and Y axes. Sets values for current lists.

WINDOW

ZBox

from the

menu. The different cursor at the center of

ZOOM

WINDOW

variables.

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: You can cancel pressing

‘

any time before you press

ZBox

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

You can repeat steps 2 through 4 to do another press

‘

3-16 Function Graphing

ZBox

to replot the graph.

. To cancel

ZBox

Zoom In, Zoom Out

Zoom In

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

XFact

and

settings determine the

YFact

extent of the zoom.

1. After checking or changing

from the

ZOOM

menu.

XFact

and

(page 3.20), select

YFact

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

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

viewing

WINDOW

, then press

The TI.82 adjusts the viewing the

WINDOW

variables, and replots the selected functions, centered on

WINDOW

XFact

and

the cursor location.

3. To zoom in on the graph again:

Zoom Out

The procedure for

To zoom in at the same point, press

To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing

Zoom Out

is the same as for

WINDOW

Zoom In

and then press

Zoom Out

ZOOM

, updates

YFact

Zoom In

Leaving Zoom In or Zoom Out

To leave

Zoom In

Select another screen by pressing the appropriate key, such as

Press y

QUIT

to return to the Home screen.

Zoom Out

Function Graphing 3-17

ZDecimal

variables to preset values that set

replots the functions immediately, updating the

and

equal to .1 and defining the

and Y value of each pixel as one decimal.

Xmin = M4.7 Ymin = M3.1 Xmax = 4.7 Ymax = 3.1 Xscl = 1 Yscl = 1

ZSquare

on the current that

Yscl

replots the functions immediately, redefining the

@X=@

WINDOW

. This makes the graph of a circle look like a circle.

variables, but adjusted in only one direction so

remain unchanged. 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

variables to the standard values:

Xmin = M10 Ymin = M10 Xmax = 10 Ymax = 10 Xscl = 1 Yscl = 1

ZTrig

replots the functions immediately, updating the

ZTrig

preset values appropriate for trig plotting functions. In are:

Xmin = M(47à24) Xmax = (47à24) Xscl = p/2 Yscl = 1

Ymin = M4 Ymax = 4

WINDOW

Radian

based

and

Xscl

variables to

these

MODE

ZInteger

ZInteger Yscl=10

redefines the viewing

, replotting the functions after you move the cursor to the point that

you want as the center of the new

ZoomStat

redefines the viewing

WINDOW

X=1

and

and press

so that all statistical data points are displayed. For one-variable plots (histograms and box plots), only and

TRACE

are adjusted. If the top of the histogram is not shown, use

Xmax

to determine the value for

Ymax

3-18 Function Graphing

Y=1

Xscl=10

, and

Xmin

Using ZOOM MEMORY

ZPrevious allows you to return to the WINDOW displayed prior to the previous ZOOM. ZoomSto stores the values of the current WINDOW variables to userdefined ZOOM MEMORY variables. ZoomRcl changes the WINDOW to the values stored with ZoomSto.

ZOOM MEMORY Menu

ZOOM MEMORY 1: ZPrevious 2: ZoomSto 3: ZoomRcl 4: SetFactors

ZPrevious

When you select replotted using the previous

ZoomSto

ZOOM

To store the current viewing

ZOOM MEMORY

of the current variables:

ZXmin, ZXmax, ZXscl, ZYmin, ZYmax

immediate, there is no prompting on the display.

These variables are global; they apply to all graphing modes. For example, changing the value of

The user-defined store to them the first time.

Uses previous viewing Stores user-defined Recalls user-defined

…

Changes

WINDOW

from the

variables of the graph displayed prior to the

ZPrevious

WINDOW

Zoom In, Zoom Out

ZOOM MEMORY

factors.

menu, the graph is

that you did.

WINDOW

, select

ZoomSto

from the

menu. The graph is displayed if necessary, and the values

WINDOW

variables are stored in the user-defined

, and

ZXmin

WINDOW

variables contain the standard values until you

Func

also changes it in

MODE

. The action is

ZYscl

ZOOM

Par

MODE

ZoomRcl

To view the selected graphing functions in the user-defined select

ZoomRcl

from the

ZOOM MEMORY

menu. The

WINDOW

are updated with the user-defined values, and the graph is plotted.

Using ZOOM MEMORY from the Home Screen or a Program

From the Home screen or a program, you can store directly to any of the user-defined

From a program, you can select the the

ZOOM MEMORY

ZOOM

variables.

menu.

ZoomSto

ZoomRcl

Function Graphing 3-19

WINDOW

variables

instructions from

Setting 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

than or equal to 1. They define the magnification or reduction factor used to

Zoom In

Checking XFact and YFact

To review the current values of the

ZOOM MEMORY

values shown are the standard values).

Changing XFact and YFact

To change

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

Position the cursor over the digit you want to change. Then type over it or use { to delete it.

are positive numbers (not necessarily integers) greater

Zoom Out

XFact

menu. The

YFact

around a point.

and

XFact

ZOOM FACTORS

, select

YFact

screen appears (the

SetFactors...

from

Leaving ZOOM FACTORS

To leave

ZOOM FACTORS

Select another screen by pressing the appropriate key, such as

Press y

QUIT

3-20 Function Graphing

to return to the Home screen.

Using CALC (Calculate) Operations

Pressing y to analyze the current graph functions. You are prompted to specify the function(s), interval, and point.

CALCULATE Menu

CALCULATE 1: value 2: root 3: minimum 4: maximum 5: intersect 6: dy/dx 7:‰f(x)dx

value

1. Select

(above

CALC

evaluates currently selected functions for a specified value of X.

value

a prompt for you to enter

2. Enter a real value for X between

expression). Note: When there is a value entered for the value; when there is no value,

3. Press

at the entered have selected

) accesses a menu with operations you can use

Calculates function value for given X. Finds root of function. Finds minimum of function. Finds maximum of function. Finds intersection of functions. Finds numeric derivative of function. Finds numeric integral of function.

from the

menu. The current graph is displayed, with

CALC

Xmin

‘

and

cancels

(which can be an

Xmax

value

‘

. The result cursor is on the first selected function in the list

and the coordinate values are displayed (even if you

CoordOff

on the

WINDOW FORMAT

screen).

4. Press † or } to move the cursor between functions at the entered

value. When | or ~ are pressed, the free-moving cursor appears. It cannot necessarily move back to the

value.

clears

Function Graphing 3-21

root

(

CALC

item 2) uses

root

-intercept) of a function. Selecting good values for the bounds and a guess

(Chapter 2) to find the root (zero or

solve(

help it find the correct root and find it more quickly.

1. Select

prompt to enter

root

from the

Lower Bound

menu. The current graph is displayed, with a

CALC

2. Use † or } to move the cursor to the function for which you want to

find the root.

3. Move the cursor to the

interval and press

value you want for the lower bound of the

. A

indicator at the top of the display shows

the lower bound.

4. Set the upper bound in the same way. An indicator shows the upper

bound.

5. You are prompted for a

to help the TI.82 find the correct root

Guess

and to find it more quickly.

6. Use | or ~ to move the cursor to a point near the root of the function,

between the bounds. Press

The result cursor is on the solution and the coordinate values are displayed (even if you have selected

CoordOff

on the

WINDOW FORMAT

When you press |, ~, }, or †, the free-moving cursor appears.

3-22 Function Graphing

screen).

minimum, maximum

(

minimum

CALC

item 3) and

maximum

(

item 4) find the minimum or

CALC

maximum of a function in a specified interval to a tolerance of 1

1. Select

minimum

maximum

from the

menu. The current graph

CALC

is displayed.

2. Set

Lower Bound, Upper Bound

, and

as described for

Guess

The result cursor is on the solution and the coordinate values are displayed (even if you have selected

CoordOff

on the

WINDOW FORMAT

When you press |, ~, }, or †, the free-moving cursor appears.

intersect

(

intersect

item 5) uses

CALC

(Chapter 2) to find the intersection of

solve(

two functions. The intersection must appear on the display.

1. Select

intersection

and you are prompted to select the

from the

menu. The current graph is displayed

CALC

First curve

root

screen).

2. Use † or } to move the cursor to the first function and press

3. Use † or } to move the cursor to the second function and press

The result cursor is on the solution and the coordinate values are displayed (even if you have selected

CoordOff

on the

WINDOW FORMAT

screen).

When you press |, ~, }, or †, the free-moving cursor appears.

Function Graphing 3-23

dy/dx

(numerical derivative,

dy/dx

(slope) of a function at a point with H = 1

1. Select

dy/dx

from the

CALC

item 6) finds the numerical derivative

CALC

menu. The current graph is displayed.

2. Move the cursor to the X value at which you want to calculate the

derivative and press

The result cursor is on the solution and the coordinate values are displayed (even if you have selected

CoordOff

on the

WINDOW FORMAT

When you press |, ~, }, or †, the free-moving cursor appears.

‰

f(x)dx

‰

(numerical integral,

f(x)dx

function a specified interval. It uses the

1. Select

‰

from the

f(x)dx

a prompt to enter

Lower Bound

item 7) finds the numerical integral of a

CALC

menu. The current graph is displayed, with

CALC

function, with a tolerance of

fnInt(

2. Use † or } to move the cursor to the function for which you want to

calculate the integral.

3. Set

Lower Limit

and

Upper Limit

as described for

root

The integral value is displayed and the integrated area is shaded. When you press |, ~, }, or †, the free-moving cursor appears.

screen).

Note: The shaded area is a drawing. Use invokes Smart Graph to clear the shaded area. (Chapter 8)

3-24 Function Graphing

ClrDraw

or any change that

Chapter 4: Parametric Graphing

This chapter describes how to graph parametric equations on the TI.82. Before doing parametric graphing, you should be familiar with Chapter 3, Function Graphing.

Chapter Contents

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

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

...........

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

4-2 4-3 4-6

Parametric Graphing 4-1

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 position 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 z. Press † † † ~

MODE

Par

to select

For initial velocity v0 and angle q, the horizontal component of the position of the ball as a function of time is X(t)=tv component is Y(t)=tv constant g is 9.8 m/sec

2. Press o. Press 15 (to select ¡)

„ ™

to define the X portion of the

parametric equation in terms of

9.8

¥ 2 ¤

„ ˜

60 y

„ ¡ Í

3. Press 15

¹ £

cosq. The vertical

sinq–(gà2)t2. The gravity

(to select ¡)

ANGLE

60 y

ANGLE

to define the

portion.

4. Press

then enter the

. Press † to move to

WINDOW

variables appropriate

Tmin

for this problem.

Tmin=0 Xmin=-2 Ymin=-2 Tmax=3 Xmax=25 Ymax=10 Tstep=.02 Xscl=5 Yscl=5

5. Press

to graph the position of the ball as

function of time.

Tracing begins at

. As you press ~ to trace

Tmin

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

(distance),

(height), and T (time) are displayed at the bottom of the screen.

and

4-2 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 six pairs of parametric equations can be defined and graphed at a time.

Defining a Parametric Graph

The steps for defining a parametric graph are the same as those for defining a function graph. Differences are noted below.

Setting Parametric Graph Modes

Press z to display the you must select

before you enter

Par

components of parametric equations. Also, you usually should select

Connected

Displaying Parametric Equations

After selecting

to obtain a more meaningful

Par

MODE

screen.

settings. To graph parametric equations,

MODE

WINDOW

variables or enter the

graph.

Par

, press o to display the parametric Y= edit

On this screen, you display and enter both X and Y components. TI.82 has six equations, each defined in terms of

Defining Parametric Equations

Follow the same procedures as for

graphing to enter the two

Func

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

defines the independent variable as T.)

MODE

, to enter the parametric variable

Parametric Graphing 4-3

. (

„

Par

Selecting Parametric Equations

Only the selected parametric equations are graphed. The = sign on both components of selected equations is highlighted. 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 The status on both the

sign on either the X or Y component and press

and Y components is changed.

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

Setting WINDOW Variables

Press

WINDOW

standard values in

Tmin=0 Tmax=6.2831853 Tstep=.1308996 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1

to display the current

variables define the viewing

MODE

Radian

Smallest T value to evaluate

…

Largest T value to evaluate (2p)

…

value increment (pà24)

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

WINDOW

variable values. The

. The values shown are the

You may want to change the T sufficient points are plotted.

4-4 Parametric Graphing

WINDOW

variable values to ensure that

Setting the WINDOW FORMAT

p ~

Press

to display the current

formats are shared with the other graphing modes.

Displaying a Graph

When you press It evaluates both the to The

in intervals of

Tmax

WINDOW

, the TI.82 plots the selected parametric equations.

and the Y component for each value of T (from

) and then plots each point defined by X and Y.

Tstep

variables define the viewing

As a graph is plotted, the TI.82 updates X, Y, and T.

Smart Graph applies to parametric graphs.

WINDOW Variables and Y-VARS Menus

From the Home screen, 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.

Store parametric equations.

Store values directly to

WINDOW

WINDOW FORMAT

WINDOW

variables.

settings. The

Tmin

Parametric Graphing 4-5

Exploring a Parametric Graph

As in Function graphing, three tools are available for exploring a graph: using the free-moving cursor, tracing an equation, and zooming.

Free-Moving Cursor

The free-moving cursor works in

TRACE

graphing. In

FORMAT

and

TRACE

CoordOn

are updated, and R and q are displayed.)

lets you move the cursor along the equation one

RectGC

FORMAT

) the values of X and Y. (In

When you begin a trace, the cursor is on the first selected equation at The number of the equation shows in the upper right of the display.

In the values of updated, and calculated from

RectGC

FORMAT, TRACE

, and T. (In

X, Y

, q, and T are displayed.) The X and Y (or R and q) values are

updates and displays (if

If the cursor moves off the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

y |

and y ~ move the

cursor remains in the same location if you leave

TRACE

if Smart Graph has not caused the graph to be replotted.

QuickZoom is available in

Par

graphing just as it does in

Par

Func

, moving the cursor updates and displays (if

PolarGC

FORMAT

PolarGC

FORMAT

Tstep

FORMAT

, X, Y, R, q and T are

, X, Y, R,

at a time.

CoordOn

cursor five plotted points at a time. The

and return,

TRACE

graphing, but panning is not.

Tmin

)

ZOOM

operations work in

ZOOM

the

X (Xmin, Xmax

, and variables are affected. T not affected, except when you select

= pà24).

CALC

Tstep

, and

ZTmax

operations work in

CALC

ZOOM MEMORY

ZTstep

operations available in

4-6 Parametric Graphing

graphing as they do in

Par

) and Y (

Xscl

WINDOW

Ymin, Ymax

variables (

ZStandard (Tmin

variables in

graphing as they do in

Par

graphing are

Par

Func

, and

Yscl

Tmin, Tmax

= 0,

graphing include

Par

Func

value, dy/dx, dy/dt

graphing. Only

)

WINDOW

, and

Tmax

graphing.

, and

Tstep

= 2p, and

ZTmin

dx/dt

) are

CALC

Chapter 5: Polar Graphing

This chapter describes how to graph polar equations on the TI.82. Before doing polar graphing, you should be familiar with Chapter 3, Function Graphing.

Chapter Contents

Getting Started: Polar Rose Defining and Displaying a Polar Graph Exploring a Polar Graph

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5-2 5 5

Polar Graphing 5-1

Getting Started: Polar Rose

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

The polar equation A sin Bq graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B.

1. Press z. Press † † † ~ ~

Pol

. Choose the initial settings for the

MODE

other modes (the choice at the beginning of each line).

2. Press o to display the polar Press

3. Press

„ Í

2.5

6 to select

ZStandard

equation in the standard viewing

edit screen.

to define

to graph the

WINDOW

Notice that the graph shows only five petals of the rose and that the rose does not appear symmetrical. This is because the standard

WINDOW

defines the

pixels) as square and sets

4. Press

5. Press

Press † †

max

to display the

5 to select

WINDOW

to increase the value of

max=2

WINDOW

ZSquare

(rather than the

and plot the

graph.

6. Continue, changing

and B to other values.

to select

settings.

5-2 Polar Graphing

Defining and Displaying a Polar Graph

Polar equations are defined in terms of the independent variable q. Up to six polar equations can be defined and graphed at a time.

Defining a Polar Graph

The steps for defining a polar graph are the same as those for defining a function graph. Differences are noted below.

Setting Polar Graph Modes

Press z to display the must select

before you enter

Pol

equation. Also, you usually should select meaningful

Displaying Polar Equations

After selecting

Pol

graph.

Pol

MODE

On this screen, you display and enter polar equations. The TI.82 has six equations, each defined in terms of

settings. To graph polar equations, you

MODE

WINDOW

variables or enter a polar

Connected

to obtain a more

, press o to display the polar Y= edit screen.

Defining Polar Equations

Follow the same procedures as for

graphing to define a new polar

Func

equation. The independent variable in a polar equation is

„

, rather than pressing

(

Pol

Selecting Polar Equations

defines the independent variable as q.)

MODE

, to enter the polar variable

Only the selected polar equations are graphed. The = sign on selected equations is highlighted. You may select any or all of the equations on the polar

edit screen.

To change the selection status of a polar equation, press | to move the cursor onto the

sign and press

Note: When you edit an equation, that equation is selected automatically.

Polar Graphing 5-3

. You may press

Setting WINDOW Variables

Press

WINDOW

to display the current

variables define the viewing

standard values in

min=0

max=6.2831853

step=.1308996 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1

… …

variable values. The

WINDOW

. The values shown are the

Radian

MODE

WINDOW

Smallest q value to be evaluated Largest q value to evaluate (2p) Increment between q values (pà24) 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

You may want to change the q

WINDOW

sufficient points are plotted.

Setting the WINDOW FORMAT

p ~

Press

to display the current

formats are shared with the other graphing modes.

variable values to ensure that

WINDOW FORMAT

settings. The

5-4 Polar Graphing

Displaying a Graph

When you press evaluates

, the TI.82 plots the selected polar equations. It

for each value of q (from

min

in intervals of

max

and then plots each point.

As a graph is plotted, the TI.82 updates

X, Y, R

, and q.

Smart Graph applies to polar graphs.

Note that the free-moving cursor displays X and Y coordinate values if the

WINDOW FORMAT

PolarGC

WINDOW Variables and Y-VARS Menus

WINDOW FORMAT

setting is the default

. To see R and q, select

RectGC

From the Home screen, you can:

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

Select or deselect polar equations from a program.

Store polar equations.

Store values directly to

WINDOW

variables.

step

)

Polar Graphing 5-5

Exploring a Polar Graph

As in function graphing, three tools are available for exploring a graph: using the free-moving cursor, tracing an equation, and zooming.

Free-Moving Cursor

The free-moving cursor works in

TRACE

graphing. In

FORMAT

and

TRACE

CoordOn

are updated, and R and q are displayed.)

lets you move the cursor along the equation one

RectGC

FORMAT

) the values of X and Y. (In

When you begin a trace, the cursor is on the first selected equation at The number of the equation shows in the upper right of the display.

In the values of and

RectGC

FORMAT, TRACE

, and q. (In

X, Y

and q are displayed.)

updates and displays (if

PolarGC

If the cursor moves off the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

y |

and y ~ move the

cursor remains in the same location if you leave

TRACE

if Smart Graph has not caused the graph to be replotted.

QuickZoom is available in

Pol

graphing just as it does in

Pol

Func

, moving the cursor updates and displays (if

FORMAT

PolarGC

FORMAT

step

FORMAT

, X, Y, R, and q are updated,

, X, Y, R,

at a time.

CoordOn

min

cursor five plotted points at a time. The

and return,

TRACE

graphing, but panning is not.

)

ZOOM

operations work in

ZOOM

the

X (Xmin, Xmax

, and variables are affected. The q are not affected, except when you select

and

Zqmin, Zqmax

CALC

CALC CALC

= pà24). The

step

, and

Zqstep

operations work in operations available in

5-6 Polar Graphing

graphing as they do in

Pol

) and Y (

Xscl

WINDOW

ZOOM MEMORY

Ymin, Ymax

variables (

graphing as they do in

Pol

graphing are

Pol

, and

min

ZStandard

variables in

value, dy/dx

graphing. Only

Func

)

Yscl

WINDOW

, and

max

(

= 0,

min

graphing include

Pol

graphing. The

Func

, and

max

dr/d

step

= 2p,

)

Chapter 6: Sequence Graphing

This chapter describes how to graph sequences on the TI.82. Before doing sequence graphing, you should be familiar with Chapter 3, Function Graphing.

Chapter Contents

Getting Started: Forest and Trees Defining and Displaying a Sequence Graph Exploring a Sequence Graph

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6-2 6-3 6-6

Sequence Graphing 6-1

Getting Started: Forest and Trees

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

A small forest contains 4000 trees. The new forestry plan is that each year 20% of the trees will be harvested and 1000 new trees will be planted. Will the forest disappear? Does it stabilize at a certain number of trees? If so, what is that number?

to select

1. Press z. Press † † † ~ ~ ~ select

Dot

Seq

MODE

. Press † ~

2. Press o. Each year the number of trees is 80 percent of what was there at the end of the prior year. Press

 ~

(to select

iPart

, because

the company will not harvest part of a tree) £

n-1

number of trees after each harvest. Press

1000

3. Press Press

(

function of ¬) ¤ to define the

2nd

to define the replacement trees.

. Press † to move to

4000

to define the number of trees

UnStart

at the beginning of the program.

4. Press † † †

to set

Max=50

to plot

the size of the forest over 50 years.

5. Set the other

Xmin=0 Ymin=0 Xmax=50 Ymax=6000 Xscl=10 Yscl=1000

6. Press

WINDOW

. Tracing begins at

variables:

Min

(before the forestry program began). Press ~ to trace the values year-by-year. The values for

(trees) are displayed at the bottom of the

(year) and

screen. How many years does it take to stabilize the size of the forest?

6-2 Sequence Graphing

Texas instruments TI-82 Guidebook

Specifications and Main Features

Frequently Asked Questions

User Manual

Table of Contents

Getting Started: Do This First!

Chapter 1: Operating the TI.82

Chapter 2: Math, Angle, and Test Operations

Chapter 3: Function Graphing

Chapter 4: Parametric Graphing

Chapter 5: Polar Graphing

Chapter 6: Sequence Graphing

Chapter 7: Tables

Chapter 8: DRAW Operations

Chapter 9: Split Screen

Chapter 10: Matrices

Chapter 11: Lists

Chapter 12: Statistics

Chapter 13: Programming

Chapter 14: Applications

Chapter 15: Memory Management

Chapter 16: Communication Link

Appendix A: Tables

Appendix B: Reference Information

Index

Using this Guidebook Effectively

Structure of the Guidebook

Page-Design Conventions

Information-Mapping Conventions

Reference Aids

Glossary

Getting Started: Do This First!

TI-82 Menus

Displaying a Menu

Moving from One Menu to Another

Selecting an Item from a Menu

Leaving without Making a Selection

First Steps

Entering a Calculation: Compound Interest

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 on the Graph

Finding the Calculated Maximum

Other Features

Graphing

Sequences

Tables

Matrices

Lists

Statistics

Programming

Split Screen

Chapter 1: Operating the TI-82

Turning the TI-82 On and Off

Turning the Calculator On

Turning the Calculator Off

APD™ (Automatic Power Down™)

Batteries

Setting the Display Contrast

Adjusting the Display Contrast

When to Replace Batteries

The Display

Home Screen

Displaying Entries and Answers

Returning to the Home Screen

Display Cursors

Busy Indicator

Entering Expressions and Instructions

Expressions

Entering an Expression

Multiple Entries on a Line

Entering a Number in Scientific Notation

Functions

Instructions

Interrupting a Calculation

TI-82 Edit Keys

Setting Modes