Exploring Cos(X) = Sin(X) - Texas Instruments TI-89 Manual Book

Exploring cos(x) = sin(x)

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 A .
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.
Hint: To get the "with"
operator:
Í
TI-89:
2
TI-92 Plus: È
This activity uses two methods to find where cos(x) = sin(x) for
the values of x between 0 and 3p.
Perform the following steps to observe where the graphs of the
functions and
y1(x)=cos(x)
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
4. Find the intersection point of
the two functions.
5. Note the and coordinates.
x y
(Repeat steps 4 and 5 to find
the other intersections.)
Perform the following steps to solve the equation
respect to
x .
1. On the Home screen, enter
solve(sin(x)= cos(x),x)
The solution for is where
x
@n1 is any integer.
2. Using the and
ceiling()
functions, find the ceiling and
floor values for the
intersection points as shown.
3. Enter the general solution for
and apply the constraint for
as shown.
@n1
Compare the result with
Method 1.
intersect.
y2(x)=sin(x)
.
p.
.
A:ZoomFit
.
floor()
x
Chapter 23: Activities
with
sin(x)=cos(x)
389