## Math 117 - Chapter 4 Study Guide

1. Draw a triangle and identify the type of problem (SAS, SSA, etc). Solve if possible. Round your final answers to one decimal place. (While final answers should be rounded to one decimal place, be careful about rounding intermediate steps). Look at problems 4.1.1-16 and 4.2.1-16. Be aware of the ambiguous case.
2. Find the area of the triangle. Look at problems 4.1.17-22.
3. Draw a triangle and identify the type of problem (SAS, SSA, etc). Solve if possible. Round your final answers to one decimal place. (While final answers should be rounded to one decimal place, be careful about rounding intermediate steps). Look at problems 4.1.1-16 and 4.2.1-16. Be aware of the ambiguous case.
4. Consider the given complex number. Graph the complex number and find its absolute value. Look at problems 4.4.1-8, 13-20
5. Draw a triangle and identify the type of problem (SAS, SSA, etc). Solve if possible. Round your final answers to one decimal place. (While final answers should be rounded to one decimal place, be careful about rounding intermediate steps). Look at problems 4.1.1-16 and 4.2.1-16. Be aware of the ambiguous case.
6. Convert the complex number from standard form into trigonometric form. Look at problems 4.4.13-20
7. Convert the complex number from trigonometric form to standard form. Look at problems 4.4.21-28
8. Find all complex solutions to the equation. Look at problems 4.4.67-72
9. Simplify the following and write the answer in standard form for a complex number. Three parts. Look at problems 4.3.1-44
10. Find the component form of the vector given the initial and terminal points. Look at problems 4.6.1-6
11. Given two vectors, find the angle between the vectors. Look at problems 4.6.63-68.
12. Perform the indicated operation on the complex number in trigonometric form. After performing the operation, write your answer in standard form. Angles have been chosen so the answers have exact values. Three parts. Look at problems 4.4.29-32, 45-46
13. Application of vectors. Look at problems 4.5.25-30.
14. Perform the indicated calculations for the given vectors. Express your answer as a linear combination of the i and j vectors. Look at problems 4.6.45-48
15. You are given the magnitude of two vectors and the angle between them. Find the magnitude of the resultant vector using the law of cosines and then angle the resultant vector forms with the vector u using the law of sines. Look at problems 4.5.17-24
16. Perform the indicated calculations for the given vectors. Look at problems 4.6.9-26

### Notes:

• Some of the problems are directly from the text.
• 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.

Points for each problem
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Tot. 8 5 8 5 8 4 4 5 9 4 5 9 5 6 6 9 100