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.