Review Test 3 Solutions: (not guaranteed)

Chapter 7

1. Prove the following:

Therefore this is an identity equation.

2. Prove the following:

Therefore this is an identity equation.

3. Prove the following:

Therefore this is an identity equation.

4. Prove:

Therefore this is an identity equation.

5. Prove:

Therefore this is an identity equation.

6. Evaluate without the use of a calculator:

a. ()

b. Use the half angle formula:

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

a.

=

b. sin2x + cos 2x

c.

8. 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

See the book.

9. Find the exact value of .

Ans:

10.

Draw a picture:

Ans: -4/3

11.

This is like the where and.

and

=

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

a.

b. =

Since Beta is in quadrant 2, half of that is in quadrant one. Therefore we use the positive portion.

c.

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

a.

The period of the function is .

Hence the solutions on are

All solutions are x = where n is an element of the integers.

a.

On :

All solutions:

b.

On :

All solutions:

c.

On :

All solutions:

d.

You need to use your calculator since this is a combination of trigonometric functions and polynomial functions.

14. Write the following complex number in trigonometric form:

a. 1 + i

b.

15. Write the following complex number in standard form.

a.

b.

Use the half angle formula:

16. Multiply the two numbers above.

17. Divide.

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

r = 5

19. Find all fourth roots of

r = 8. n = 4.

Distance between roots is