Review Test 3

Chapter 7

1. Harmonic Motion Problems:

2. Prove the following:

3. Prove the following:

4. Prove the following:

5. Prove:

6. Prove:

7. Evaluate without the use of a calculator:

a. ()

b.

8. Rewrite the following as a trigonometric expression of 1 number.

a.

b. sin2x + cos 2x

c.

9. State the domain and range of f(x) = arcsin(x), g(x) = arccos(x) and h(x) = arctan(x). Then sketch the graph of each function

10. Find the exact value of .

11.

12.

13. Given the following information, and lies in quadrant I, and lies in quadrant II. Determine the following:

a.

b.

c.

14. Solve the following equations on all real numbers, and then on the interval.

a.

b.

c.

d.

e.

15. Write the following complex number in trigonometric form:

a. 1 + i

b.

16. Write the following complex number in standard form.

a.

b.

17. Multiply the two numbers above.

18. Divide .

19. Given , find . Put your answer in trigonometric form.

20. Find all fourth roots of