## Math 117 - Final Exam Study Guide

1. Find the exact values for each of the six trigonometric functions for the specified angle and then find the angle.
2. Solve the right triangle.
3. Given the value of one of the trigonometric functions and the quadrant the angle lies in, give the values of the other five trigonometric functions.
4. Determine the amplitude, period, and phase shift of the function and sketch the graph of the function.
5. Find the length of an arc on a circle with the given radius and central angle.
6. Simplify the trigonometric expressions completely.
7. Prove the identity. Work on one side of the identity only.
8. Solve, finding all solutions in the interval [0,2π)
9. Evaluate the expressions using inverse trig functions.
10. Draw a triangle and identify the type of problem. Then solve the triangle if possible.
11. Simplify the expression involving complex numbers and write the answer in standard form.
12. Convert the complex number into trigonometric form.
13. Perform the operation involving complex numbers in trigonometric form and write the exact value in standard notation.
14. Find all complex solutions of the equation. Leave your answer in trigonometric form.
15. Perform the indicated operations with the vectors.
16. Find the center, vertices, and foci and then sketch the graph of the conic.
17. Find the equation of the conic that satisfies the given conditions.
18. Use the discriminant to identify the conic as an ellipse, hyperbola, or parabola.
19. Graph the polar equation.
20. Find the polar equation of the conic with the focus at the pole and the given eccentricity and directrix.
21. Use the polar equation to find the eccentricity and identify as a parabola, ellipse, or hyperbola. Find the distance and direction from the pole to the directrix. Find the vertex or vertices. Graph the equation.
22. Convert the rectangular equation into a polar equation and solve for r.
23. Find all real or complex solutions to the system of equations.
24. Use properties of logarithms to expand the single logarithm into the sum, difference, and/or constant multiples of logarithms.
25. Use properties of logarithms to combine into a single logarithm.
26. Solve the exponential and logarithmic equations.

### Notes:

• Some of the problems are directly from the text.
• Most of the problems are like those off of previous tests.
• There is no material from chapter 1 on the test.

Points for each problem
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 5 10 8 5 10 6 6 10 16 6 5 6 14 15 16 17 18 19 20 21 22 23 24 25 26 Tot 6 9 8 6 5 5 6 6 12 6 6 6 12 200