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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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

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
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
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? _________