Texas-instruments PLUS TI-89 User Manual download pdf (Page 406)

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101

Chapter 23: Activities 389

23ACTS.DOC TI-89/TI-92 Plus: Activities (English) Susan Gullord Revised: 02/23/01 1:24 PM Printed: 02/23/01 2:20 PM Page 389 of 26

Perform the following steps to observe where the graphs of the

functions

y1(x)=cos(x)

and

y2(x)=sin(x)

intersect.

1. In the Y= Editor, set

y1(x)=cos(x

) and

2(x)=sin(x)

2. In the Window Editor, set

xmin=0

and

xmax=3

3. Press

„

and select

A:ZoomFit

4. Find the intersection point of

the two functions.

5. Note the

and

coordinates.

(Repeat steps 4 and 5 to find

the other intersections.)

Perform the following steps to solve the equation

sin(x)=cos(x)

with

respect to

1. On the Home screen, enter

solve(sin(x)= cos(x),x)

The solution for

is where

@n1

is any integer.

2. Using the

ceiling()

and

floor()

functions, find the ceiling and

floor values for the

intersection points as shown.

3. Enter the general solution for

and apply the constraint for

@n1

as shown.

Compare the result with

Method 1.

Exploring cos(x) = sin(x)

This activity uses two methods to find where

cos(x) = sin(x) for

the values of x between 0 and 3

Method 1:

Graph Plot

Hint:

Press

‡

and select

5:Intersection.

Respond to

the screen prompts to select

the two curves, and the

lower and upper bounds for

intersection

Method 2:

Symbolic

Manipulation

Hint:

Move the cursor into

the history area to highlight

the last answer. Press

to copy the result of

the general solution.

Hin

t: To get the “with”

operator:

89:

92 Plus:

1 2 ... 401 402 403 404 405 406 407 408 409 410 411 ... 622 623

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Texas-instruments PLUS TI-89 User Manual Page 406

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