## Math 117 - Chapter 3 Study Guide

1. Simplify the expressions. Look at problems 3.1.17-30. Three parts.
2. First write the following as a trigonometric function of a single angle; then evaluate. Look at problems 3.1.57-60.
3. Evaluate the value exactly. Use the half-angle or sum/difference of two angle formulas. Look at problems 3.1.51-56 and 3.2.17-22.
4. Use the given identity to evaluate the expression.
Example, if sin x cos y = 1 / 2 [ sin (x-y) + sin (x+y) ], then find sin 150° cos 120°.
5. Given the sine or cosine of a value and the quadrant in which it lies, find other values using double and half-angle identities. Look at problems 3.2.23-26. Two parts.
6. Use the calculator to find the inverse function value to the nearest tenth of a degree. Look at problems 3.4.21-32.
7. Find each of the inverse functions exactly in both radians and degrees. Two parts. Look at problems 3.4.1-20.
8. Evaluate the expression involving functions and inverse functions. Three parts. Look at problems 3.4.37-52.
9. Solve, finding all solutions in the interval [ 0, 2π). Two parts. Look at problems 3.5.24-38.
10. Prove the identity, two parts. Look at problems 3.3.1-30.
11. Prove the identity, two parts. Look at problems 3.3.1-30.

### Notes:

• Give EXACT VALUES unless otherwise noted (problem 6)
• The test was derived by looking at the chapter review and making problems similar to those problems, so you may want to look at the chapter review first and then if you have problems with those, go back to the problems given above as references.
• There is a take home portion of the exam consisting of proofs of identities. Work on one side of the identity only. This is worth 16 points and is due the day of the in-class exam.
• Problems 10 and 11 are both to prove identities. I split it into two problems so the instructions weren't split across pages. You may think this is excessive on the proofs, but I originally had a second "simply" problem (like #1) that I decided to give you the answers to and just make it a "prove" problem instead, so it's actually easier since you know where you're headed.
• You may NOT have a formula sheet on the in-class test. However, feel free to use one on the take home exam.

### Points for each problem

 # 1 2 3 4 5 6 7 8 9 10 11 Tot. pts 10 5 5 5 10 5 6 12 10 8 8 84