Review for final

1. Describe how you can find the relationship among three sides of a right triangle when the angles are and

2. For Find (a) (b)

3. If and Find

4. Find the inverse function for if it exists. If they exist, graph and together.

5. If the graph of is shown below:

1. Sketch the graph of

2. Sketch the graph of

3. Sketch the graph of

4. Sketch the graph of

6. If or Then

1. find the domain and range for

2. sketch the graph of

7. If or Then

1. find the domain and range for

2. sketch the graph of

8. If Then

1. find the domain and range for

2. sketch the graph of

9. If find the inverse functions for and respectively.

10. If find the inverse functions for and respectively.

11. Find the exact vaule of the expression without using a calculator

12. Write an algebraic expression that is equivalent to the given expression.

13. Prove the followings graphically:

14. Prove algebraically.

15. Prove algebraically.

16. Prove

17. If the graph of is given, then

1. find the vertical asymptotes for

2. sketch by changing the units from

18. Simplify the following expressions algebraically first and prove your results graphically with explanations

19. page 221, 81-88. Trig substitutions.

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