Texas Instruments TI-82 STATS Manuale utente

Part I: Texas Instruments TI-82 Graphics Calculator

I.1 Getting started with the TI-82

I.1.1 Basics: Press the ON key to begin using your TI-82 calculator. If you need to adjust the display

contrast, first press 2nd,then press and hold (the up arrow key) to lighten or (the down arrow key)

to darken. As you press and hold or , an integer between 0 (lightest) and 9 (darkest) appears in the

upper right corner of the display. When you have finished with the calculator, turn it off to conserve battery

power by pressing 2nd and then OFF.

Check the TI-82’s settings by pressing MODE. If necessary, use the arrow keys to move the blinking cursor

to a setting you want to change. Press ENTER to select a new setting. To start, select the options along the

left side of the MODE menu as illustrated in Figure I.1: normal display, floating decimals, radian measure,

function graphs, connected lines, sequential plotting, and full screen display. Details on alternative options

will be given later in this guide. For now, leave the MODE menu by pressing CLEAR.

Figure I.1: MODE menu Figure I.2: Home screen

I.1.2 Editing: One advantage of the TI-82 is that up to 8 lines are visible at one time, so you can see a long

calculation. For example, type this sum (see Figure I.2):

Then press ENTER to see the answer.

Often we do not notice a mistake until we see how unreasonable an answer is. The TI-82 permits you to

redisplay an entire calculation, edit it easily, then execute the corrected calculation.

Suppose you had typed as in Figure I.2 but had not yet pressed ENTER,when you realize

that 34 should have been 74. Simply press (the left arrow key) as many times as necessary to move the

blinking cursor left to 3, then type 7 to write over it. On the other hand, if 34 should have been 384, move

the cursor back to 4, press 2nd INS (the cursor changes to a blinking underline) and then type 8 (inserts at

the cursor position and the other characters are pushed to the right). If the 34 should have been 3 only, move

the cursor to 4 and press DEL to delete it.

Technology Tip: To move quickly to the beginning on an expression you are currently editing, press (the

up arrow key); to jump to the end of that expression, press (the down arrow key).

Even if you had pressed ENTER,you may still edit the previous expression. Press 2nd and then ENTRY to

recall the last expression that was entered. Now you can change it. In fact, the TI-82 retains many prior

entries in a “last entry” storage area. Press 2nd ENTRY repeatedly until the previous line you want replaces

the current line.

12 34 56

12345678910 11 12 13 14 15 16 17 18 19 20

Technology Tip: When you need to evaluate a formula for different values of a variable, use the editing

feature to simplify the process. For example, suppose you want to find the balance in an investment account

if there is now $5000 in the account and interest is compounded annually at the rate of 8.5%. The formula for

the balance is where principal, rate of interest (expressed as a decimal), number

of times interest is compounded each year, and number of years. In our example, this becomes

Here are the keystrokes for finding the balance after 5, and 10 years (results are

shown in Figure I.3).

Years Keystrokes Balance

35000 (1 + .085) ^ 3 ENTER $6386.45

52nd ENTRY 5 ENTER $7518.28

10 2nd ENTRY 10 ENTER $11,304.92

Figure I.3: Editing expressions

Then to find the balance from the same initial investment but after 5 years when the annual interest rate is

7.5%, press these keys to change the last calculation above: 2nd ENTRY DEL 5 7 ENTER.

I.1.3 Key Functions: Most keys on the TI-82 offer access to more than one function, just as the keys on a

computer keyboard can produce more than one letter (“g” and “G”) or even quite different characters (“5”

and “%”). The primary function of a key is indicated on the key itself, and you access that function by a

simple press on the key.

To access the second function to the left above a key, first press 2nd (the cursor changes to a blinking ) and

then press the key. For example, to calculate press 2nd 25 ENTER.

When you want to use a letter of other characters printed to the right above a key, first press ALPHA (the

cursor changes to a blinking A) and then the key. For example, to use the letter K in a formula, press

ALPHAK. If you need several letters in a row, press 2ndA-LOCK,which is like CAPS LOCK on a computer

keyboard, and then press all the letters you want. Remember to press ALPHA when you are finished and

want to restore the keys to their primary functions.



25,

➞

t3,5000



1.085)

.t

nrPP



1r

nt

I.1.4 Order of Operations: The TI-82 performs calculations according to the standard algebraic rules.

Working outwards from inner parentheses, calculations are performed from left to right. Powers and roots

are evaluated first, followed by multiplications and divisions, and then additions and subtractions.

Note that the TI-82 distinguishes between subtraction and the negative sign. If you wish to enter a negative

number, it is necessary to use (-) key. For example, you would evaluate by pressing

(-) 5 – (4 (-) 3 ) ENTER to get 7.

Enter these expressions to practice using your TI-82.

Expression Keystrokes Display

7 – 5 3 ENTER -8

(7 – 5) 3 ENTER 6

120 – 10 ENTER 20

(120 – 10)ENTER 12100

24 ÷ 2 ^ 3 ENTER 3

(24 ÷ 2) ^ 3 ENTER 1728

(7 – (-) 5 ) (-) 3 ENTER -36

I.1.5 Algebraic Expressions and Memory: Your calculator can evaluate expressions such as after

you have entered a value for N. Suppose you want Press 200 STO ALPHA N ENTER to store

the value of 200 in memory location N. Whenever you use Nin an expression, the calculator will substitute

the value 200 until you make a change by storing another number in N. Next enter the expression

by typing ALPHA N ( ALPHA N + 1 ) ÷ 2 ENTER. For you will find that

The contents of any memory location may be revealed by typing just its letter name and then ENTER. And

the TI-82 retains memorized values even when it is turned off, so long as its batteries are good.

I.1.6 Repeated Operations with ANS:The result of your last calculation is always stored in memory

location ANS and replaces any previous result. This makes it easy to use the answer from one computation

in another computation. For example, press 30 + 15 ENTER so that 45 is the last result displayed. Then

press 2nd ANS ÷9ENTER and get 5 because

With a function like division, you press the key after you enter an argument. For such functions, whenever

you would start a new calculation with the previous answer followed by pressing the function key, you may

press just the function key. So instead of 2nd ANS ÷ 9 in the previous example, you could have pressed

simply ÷9to achieve the same result. This technique also works for these functions: + – .x

-1





45 95.



N1



220,100.N200,



N1



N200.



N1







75



3



3



120 10



120 10





75



3

753



5(4 3)

Here is a situation where this is especially useful. Suppose a person makes $5.85 per hour and you are asked

to calculate earnings for a day, a week, and a year. Execute the given keystrokes to find the person’s incomes

during these periods (results are shown in Figure I.4.):

Pay period Keystrokes Balance

8-hour day 5.85 8 ENTER $46.80

5-day week 5 ENTER $234

52-week year 52 ENTER $12,168

Figure I.4: ANS variable

I.1.7 The MATH Menu: Operators and functions associated with a scientific calculator are available either

immediately from the keys of theTI-82 or by the 2nd keys.You have direct key access to common arithmetic

operations ( , 2nd ,,^,2nd ABS), trigonometric functions (SIN,COS,TAN) and their inverses

( 2nd SIN ,2nd COS ,2nd TAN ),exponential and logarithmic functions (LOG,2nd ,LN,2nd ),

and a famous constant (2nd π).

A significant difference between the TI-82 graphing calculators and most scientific calculators is that the

TI-82 requires the argument of a function after the function, as you would see a formula written in your

textbook. For example, on the TI-82 you calculate by pressing the keys 2nd 16 in that order.

Here are keystrokes for basic mathematical operations. Try them for practice on your TI-82.

Expression Keystrokes Display

2nd (3 + 4 )ENTER 5

2 + 3 ENTER 2.333333333

2nd ABS (-) 5 ENTER 5

log 200 LOG 200 ENTER 2.301029996

2.34 2nd 5 ENTER 234000

Additional mathematical operations and functions are available from the MATH menu. Press MATH to see

the various options (Figure I.5).You will learn in your mathematics textbook how to apply many of them.

As an example, calculate by pressing MATH and then either 4



or ENTER; finally

press 7ENTER to see 1.912931183. To leave MATH menu and take no other action, press 2nd QUIT or

just CLEAR.



2.34 10



5



-1



4



x-1-1-1

-1





Figure I.5: MATH menu

The factorial of a nonnegative integer is the product of all the integers from 1 up to the given integer. The

symbol for factorial is the exclamation point. So 4! (pronounced four factorial) is You

will learn more about applications of factorials in your textbook, but for now use the TI-82 to calculate 4!

The factorial command is located in the MATH menu’s PRB sub-menu. to compute 4!, press these

keystrokes: 4MATH 4 ENTER or 4MATH ENTER ENTER.

Note that you can select a sub-menu from the MATH menu by pressing either or . It is easier to press

once than to press three times to get to the PRB sub-menu.

I.2 Functions and Graphs

I.2.1 Evaluating Functions: Suppose you received a monthly salary of $1975 plus a commission of

10% of sales. Let your sales in dollars; then your wages in dollars are given by the equation

If your January sales were $2230 and your February sales were $1865, what was your income during

those months?

Here’s one method to use your TI-82 to perform this task. Press the Y= key at the top of the calculator to

display the function editing screen (Figure I.6). You may enter as many as ten different functions for the

TI-82 to use at one time. If there is already a function , press or as many times as necessary to

move the cursor to and then press CLEAR to delete whatever was there. Then enter the expression

by pressing these keys: 1975 + .10 X,T, . (The X,T, key lets you enter the variable Xeasily

without having to use the ALPHA key.) Now press 2nd QUIT to return to the main calculations screen.

Figure I.6: Y= screen Figure I.7: Evaluating a function

1975 .10xY

W1975 .10x.Wx 

123424.

Assign the value 2230 to the variable by using these keystrokes (see Figure I.7): 2230 STO X,T, .

Then press 2nd : to allow another expression to be entered on the same command line. Next press the

following keystrokes to evaluate and find January’s wages: 2nd Y-VARS 1[Function] 1[]ENTER. It

is not necessary to repeat all these steps to find the February wages. Simply press 2nd ENTRY to recall the

entire previous line, change 2230 to 1865, and press ENTER. Each time the TI-82 evaluates the function ,

it uses the current value of

Figure I.8: Function notation

Like your textbook, the TI-82 uses standard function notation. So, to evaluate when

press 2nd Y-VARS 1 1 (2230) ENTER (see Figure I.8). Then to evaluate

press 2nd ENTRY to recall the last line, change 2230 to 1865, and press ENTER.

You may also have the TI-82 make a table of values for the function. Press 2nd TblSet to set up the table

(Figure I.9). Move the blinking cursor onto Ask beside Indpnt:,then press ENTER. This configuration

permits you to input values for one at a time. Now press 2nd TABLE,enter 2230 in the Xcolumn, and

press ENTER (see Figure I.10). Continue to enter additional values for Xand the calculator automatically

completes the table with corresponding values of . Press 2nd QUIT to leave the TABLE screen.

Figure I.9: TblSet screen Figure I.10: Table of values

For a table containing values for 2, 3, 4, 5, and so on, set TblMin 1 to start at Tbl 1 to

increment in steps of 1, and both Indpnt and Depend to Auto.

Technology Tip: The TI-82 does not require multiplication to be expressed between variables, so means

It is often easier to press two or three ’s together than to search for the square key or the powers key. Of

course, expressed multiplication is also not required between a constant and variable. So, to enter

in the TI-82, you might save keystrokes and press just these keys: 2 X,T,X,T,

X,T,+3X,T,X,T,4X,T,+ 5.

2x

3x

4x5

.xxx



x1,



x1,



1865),Y





1975 .10x,Y



2230



x.Y

x

I.2.2 Functions in a Graph Window: Once you have entered a function in the Y= screen of the TI-82,

just press GRAPH to see its graph. The ability to draw a graph contributes substantially to our ability to

solve problems.

For example, here is how to graph First press Y= and delete anything that may be there by

moving with the arrow keys to or to any of the other lines and pressing CLEAR wherever necessary. Then,

with the cursor on the top line press (-) X,T,MATH 3 + 4 X,T,to enter the function (as in Figure I.11).

Now press GRAPH and the TI-82 changes to a window with the graph of (Figure I.12).

While the TI-82 is calculating coordinates for a plot, it displays a busy indicator at the top right of the

graph window.

Technology Tip: If you would like to see a function in the Y= menu and its graph in a graph window, both

at the same time, open the MODE menu, move the cursor down to the last line, and select Split screen.Your

TI-82’s screen is now divided horizontally (see Figure I.11), with an upper graph window and a lower

window that can display the home screen or an editing screen. The split screen is also useful when you need

to do some calculations as you trace along a graph. For now, restore the TI-82 to FullScreen.

Your graph window may look like the one in Figure I.12 or it may be different. Because the graph of

extends infinitely far left and right and also infinitely far up and down, the TI-82 can display

only a piece of the actual graph. This displayed rectangular part is called a viewing window. You can easily

change the viewing window to enhance your investigation of a graph.

Figure I.11: Split screen: Y= below Figure I.12: Graph of

The viewing window in Figure I.12 shows the part of the graph that extends horizontally from to 10

and vertically from to 10. Press WINDOW to see information about your viewing window. Figure I.13

shows the WINDOW screen that corresponds to the viewing window in Figure I.12. This is the standard

viewing window for the TI-82.

Figure I.13: Standard WINDOW

10

yx

4x

−10

−10 10

yx

4x

yx

4x

Y

yx

4x.

The variables Xmin and Xmax are the minimum and maximum values of the viewing window. Ymin and

Ymax are its minimum and maximum values.

Xscl and Yscl set the spacing between tick marks on the axes.

Use the arrow keys and to move up and down from one line to another in this list; pressing the

ENTER key will move down the list. Press CLEAR to delete the current value and then enter a new value.

You may also edit the entry as you would edit an expression. Remember that a minimum must be less than

the corresponding maximum or the TI-82 will issue an error message.Also, remember to use the (-) key, not

– (which is subtraction), when you want to enter a negative value. Figures I.12–13, I.14–15, and I.16–17

show different WINDOW screens and the corresponding viewing window for each one.

Figure I.14: Square window Figure I.15: Graph of

To initialize the viewing window quickly to the standard viewing window (Figure I.13), press ZOOM 6

[ZStandard]. To set the viewing window quickly to a square window (Figure I.14), press ZOOM 5

[ZSquare]. More information about square windows is presented later in Section I.2.4.

Figure I.16: Custom window Figure I.17: Graph of

Sometimes you may wish to display grid points corresponding to tick marks on the axes. This and other

graph format options may be changed by pressing WINDOW to display the FORMAT menu (Figure I.18).

Use arrow keys to move the blinking cursor to GridOn; press ENTER and then GRAPH to redraw the

graph. Figure I.19 shows the same graph as in Figure I.17 but with the grid turned on. In general, you’ll want

the grid turned off,so do that now by pressing WINDOW ,use the arrow keys to move the blinking cursor

to GridOff,and press ENTER and CLEAR.

yx

4x

−10

−33

yx

4x

−10

−15 15

y-x-

Figure I.18: WINDOW FORMAT menu Figure I.19: Grid turned on for

I.2.3 Graphing Step and Piecewise-Defined Functions: The greatest integer function, written gives the

greatest integer less than or equal to a number On the TI-82, the greatest integer function is called Int and

is located under the NUM sub-menu of the MATH menu (see Figure I.5). So, calculate by

pressing MATH 4 6.78 ENTER.

To graph go into the Y= menu, move beside and press CLEAR MATH 4 X,T, GRAPH.

Figure I.20 shows this graph in a viewing window from to 5 in both directions.

Figure I.20: Connected graph of Figure I.21: Dot graph of

The true graph of the greatest integer function is a step graph, like the one in Figure I.21. For the graph of

a segment should not be drawn between every pair of successive points. You can change from

Connected line to Dot graph on the TI-82 by opening the MODE menu. Move the cursor down to the fifth

line; select whichever graph type you require; press ENTER to put it into effect, and GRAPHto see the result.

Make sure to change your TI-82 back to Connected line, because most of the functions that you will be

graphing should be viewed this way.

yx,

yxyx

−5

−55

−5

−55

5

Y

,yx,

6.786

x.x,

yx

4x

−10

−33

The TI-82 can graph piecewise-defined functions by using the options in the TEST menu (Figure I.22) that

is displayed by pressing 2nd TEST. Each TEST function returns the value 1 if the statement is true, and the

value 0 if the statement is false.

Figure I.22: 2nd TEST menu

For example, to graph the function (using Dot graph) enter the following keystrokes

Y= ( X,T, + 1) ( X,T, 2nd TEST 5 0 ) + ( X,T, – 1 ) ( X,T, 2nd TEST 4 0 ) (Figure I.23). Then

change the mode to Dot graph and press GRAPH to display the graph. Figure I.24 shows this graph in a

viewing window from to 5 in both directions.

Figure I.23: Piecewise-defined function Figure I.24: Piecewise-defined graph

I.2.4 Graphing a Circle: Here is a useful technique for graphs that are not functions, but that can be “split”

into a top part and a bottom part, or into multiple parts. Suppose you wish to graph the circle whose equation

is First solve for and get an equation for the top semicircle, and for the

bottom semicircle, Then graph the two semicircles simultaneously.

Use the following keystrokes to draw the circle’s graph. Enter as and as

(see Figure I.25) by pressing Y= CLEAR 2nd ( 36 X,T, ) ENTER CLEAR (-) 2nd

( 36 X,T, ). Then press GRAPH to draw them both.x





x









36 x



36 x

y



36 x

.y



36 x

,yx

y

36.

−5

−55

5

 x





x

1,

x1, x

≥

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