# Investigating Trigonometric Functions

I. Click on the section titled “Sine Inverse Function” (or click the tab at
the

bottom of the screen. Answer the following questions:

1. Click on “Show y = x for reflection”. Why are we interested in examining the

line y = x when dealing with inverses?________________________________

_______________________________________________________________

2. Click on “Show Sine Inverse”. Is the new inverse graph a function ? _______
How did you make

your
decision?____________________________________________________________________

3. Drag point X. Watch points A and B. What do you notice about points A and
B? ______________

________________________________________________________________________________

Using your knowledge of inverses, explain why this is happening?
__________________________

________________________________________________________________________________

4. Click on “Hide Sine Inverse”. Click on “Show Sine Inverse Function”.

5. This new graph is only a “portion” of the previous inverse graph. Why is
the sine inverse function

graph only a “portion” of the sine inverse graph?
________________________________________

_______________________________________________________________________________

6. What is the domain of this restricted graph?
____________________________________________

Over what domain of the original function was this inverse formed?
_________________________

7. What is the range of this restricted graph? ______________________________________________

8. The notation used in Sketchpad for sine inverse is sin^{−1}(x) . What other
notation can also be used

to represent sine inverse?
___________________________________________________________

9. Using the grid at the left, graph the sine inverse

function.

Be careful that your x- values in full decimal form

from Sketchpad and the x- values in radian notation

on the graph grid represent the same values.

10. Explain why the domain of this inverse function graph

was chosen as you see it in Sketchpad? ___________

___________________________________________

___________________________________________

___________________________________________

II. Click on the section titled “Cosine Inverse Function”
(or click the tab at the

bottom of the screen. Answer the following questions:

1. Click on “Show y = x for reflection”. What function name is given to the

line y = x ?____________________________________________________

2. Click on “Show Cosine Inverse”. Is the new inverse
graph a function ? _______ What is the name

of the test used to determine if the inverse of a function is itself a
function?____________________

3. Drag point X. Watch points A and B. Are the x and y values switching places? _______________

4. Click on “Hide Cosine Inverse”. Click on “Show Cosine
Inverse Function”. Again, the inverse

function graph is only a “portion” of the full inverse graph

5. What is the domain of this restricted graph?
____________________________________________

Over what domain of the original function was this inverse formed?
_________________________

6. What is the range of this restricted graph? ______________________________________________

7. Explain why the domains of the original functions over
which the sine inverse function and the

cosine inverse functions were formed are
different ._______________________________________

________________________________________________________________________________

8. The notation used in Sketchpad for cosine inverse is
cos^{−1} (x) . What other notation can also be

used to represent cosine inverse?
_____________________________________________________

9. Using the grid at the left, graph the cosine inverse

function.

Be careful that your x- values in full decimal form

from Sketchpad and the x- values in radian notation

on the graph grid represent the same values .

III. Click on the section titled “Tangent Inverse
Function” (or click the tab at the

bottom of the screen. Answer the following questions:

1. Click on “Show y = x for reflection”. Click on “Show Tangent Inverse”.

2. Is the new inverse graph a function? _______________

3. Click on “Hide Tangent Inverse”. Click on “Show

Tangent Inverse Function”.

4. What is the domain of this restricted graph? _________

Over what domain of the original function was this

inverse formed? ______________________________

5. What is the range of this restricted graph? __________

____________________________________________

6. Using the grid at the left, graph the tangent inverse

function.

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