Pre Cal Trigonometry Final Exam Study Guide
1. Find the 6 trig ratios given a triangle with side lengths or given one ratio
2. Solve a right triangle
3. Find missing side lengths or missing angles from a triangle using sine, cosine, or tangent ratios
4. Change an angle in degrees to radians and vice versa
5. Convert between DMS and decimal degree form
6. Find negative and positive coterminal angles from a given angle
7. Know how to notate all angles or angles within a given interval
8. Find arc length
9. Find area of a sector
10. Given a trig ratio in a given quadrant, be able to find all 6 trig ratios
11. Use trig hand to find the exact value of the ratio of any special angle in degrees or radians
12. Use unit circle to find the ratio of any quadrant angle in degrees or radians
13. Find and use reference angles
14. Find the amplitude, period, and phase shift of a sine or cosine function
15. Write an equation given the amplitude, period, and phase shift
16. Match the graph of any of the 6 trigonometric functions
17. Find arcsine, arccosine, and arctangent or any of the reciprocals
18. Evaluate composition of arcfunctions
19. Use the Law of Sines and Law of Cosines to solve for missing sides or angles of triangles
20. Know the ambiguous case and when it applies and how to solve for both cases
21. Determine how many triangles can satisfy the given conditions
22. Find the area of a triangle using Heron’s formula or given SAS
23. Solve a triangle
24. Use all trigonometric identities to simplify expressions: reciprocal, quotient, Pythagorean,
cofunction, odd-even, sum and difference, double-angle, power-reducing, half-angle, product-tosum, sum-to-product identities
25. Be able to substitute, FOIL, factor, conjugate trigonometric expressions to simplify them or verify
identities or find exact values
26. Solve trigonometric equations
27. Determine if a described quantity is a vector
28. Sketch a sum of two vectors
29. Find component form given an initial point and terminal point
30. Find magnitude given an initial point and terminal point
31. Add and subtract vectors and multiply a vector by a scalar
32. Find a unit vector in the same direction of a given vector
33. Find component form of a vector given a magnitude and direction angle
34. Find direction angle of a vector
35. Write a vector as a linear combination
36. Find an angle between two vectors
37. Find the dot product and know orthogonal vector
38. Graph a point or a vector in space
39. Find component form and magnitude of vectors in space
40. Find the length and midpoint of a vector in space
41. Graph points and equations on a polar graph
42. Find multiple representations of a point on a polar graph
43. Find the distance between two polar coordinates
44. Know the symmetry checks for sine and cosine functions
45. Convert rectangular coordinates to polar coordinates and vice versa
46. Convert polar equations to rectangular equation and vice versa
47. Graph complex numbers on the complex number plane
48. Convert complex numbers to polar and vice versa
49. Multiply and divide complex numbers in polar form
50. Raise a complex number to a power using DeMoivre’s theorem