Download Ms. Wong Trigonometry, Spring 2015 Final Exam Study Guide

Ms. Wong
Trigonometry, Spring 2015
Final Exam Study Guide
List of topics covered on the final exam:
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Angle Conversions (radians to degrees, degrees to radians, DMS form)*
Sketching Angles*
Finding Coterminal Angles*
Evaluating Trigonometric Expressions (in radians and in degrees)
o Given a point on the terminal side of the angle
o Given the value of another trig function of the same angle*
o Using Sum/Difference Identity*
Finding Reference Angle*
Evaluating Inverse Trigonometric Functions (arcsin, arccos, arctan)*
Law of Sines/Cosines
o Finding missing sides/angles of oblique triangles
o Finding area of triangles oblique triangles
Finding missing side/angle given a right triangle word problem
Solving Trigonometric Equations*
Writing Equations of Graphs of Trigonometric Functions*
Finding the Period of the Graph of a Trig Function given Equation*
Verifying Trigonometric Identities*
Sketching the Graph of Trigonometric Functions*
*Starred items indicate questions that will show up as WOC questions on the final exam
Name: ______________________________________________________________________
Period: ________________
Convert from degrees to radians. Leave in simplest form, no decimals.
1. 135°
2. −220°
3. 330°
4. −80°
Convert from radians to degrees.
5.
7.
5𝜋
𝜋
6. 3
6
29𝜋
5𝜋
8. 12
18
Sketch the following angles.
9. 𝜃 = 110°
11. 𝜃 =
11𝜋
4
10. 𝜃 =
7𝜋
6
12. 𝜃 = −60°
Evaluate the following.
13. csc(2.9)
15. tan (
11𝜋
6
)
4𝜋
17. sec( 3 )
14. cos(45°)
16. sin(210°)
18. cot(0.56)
Find the coterminal angles to the following angles (positive OR negative).
19. 𝜃 = 80°
21. 𝜃 =
9𝜋
5
20. 𝜃 = 270°
𝜋
22. 𝜃 = − 8
2𝜋
23. 𝜃 = −123°
24. 𝜃 = −
25. 𝜃 = 315°
26. 𝜃 = 3𝜋
3
27. Find the value of the six trigonometric functions of 𝜃 if (-1, 4) lies on its terminal side.
sin 𝜃 =
cos 𝜃 =
tan 𝜃 =
csc 𝜃 =
sec 𝜃 =
cot 𝜃 =
𝜋
𝜋
𝜋
28. Evaluate using a sum/difference identity. Note that − 12 = 6 − 4
𝜋
sin − 12 =
𝜋
cos − 12 =
𝜋
tan − 12 =
29. If csc 𝜃 = 4 and the angle lies in quadrant I, find cos 𝜃
30. Which quadrant does the angle 𝜃 lie if cos 𝜃 < 0 and cot 𝜃 > 0
For #s 31-34, find the reference angle
31. 𝜃 = 205°
32. 𝜃 =
7𝜋
33. 𝜃 = 117°
34. 𝜃 =
11𝜋
1
3
12
35. Evaluate arccos (− 2)
36. Evaluate csc −1 (2)
37. Evaluate arctan(√3)
38. Evaluate cot −1(−1)
39. Find the period of 𝑦 = −3 sin 2𝑥
40. Find the period of 𝑦 = sec 5 + 4
𝑥
41. At a point on the ground 39 meters from the foot of a tree, the measure of the angle of
elevation of the top of the tree is 42º. Find the height of the tree to the nearest meter.
42. Find to the nearest degree the measure of the angle of elevation of the sun when a girl 150cm
tall casts a shadow 43cm long.
43. Determine an equation for this graph
44. Determine an equation for this graph
45. Solve 2 sin 𝑥 + √3 = 0 on the interval [0, 2π)
46. Solve 8 cos 𝑥 − 4√2 = 0 on the interval [0, 2π)
47. Graph the function and include two periods. 𝑦 = −2 sin(4𝑥 + 𝜋)
𝜋
48. Graph the function and include two periods. 𝑦 = cos (2𝜋𝑥 − 2 ) + 1
49. Verify this identity.
50. Verify this identity.
Sec2 𝑥
tan 𝑥
= sec 𝑥 csc 𝑥
csc 𝑥 − sin 𝑥 = cos 𝑥 cot 𝑥
For #s 51-52, convert each angle measure to decimal degree form.
51. 54°45′
52. 330°25"
For #s 53-54, convert each angle measure to 𝐷°𝑀′𝑆" form.
53. −0.355°
54. 240.6°
55. Find the area of the oblique triangle given 𝐶 = 120°,
𝑎 = 4,
3
56. Given a triangle with 𝐴 = 55°,
𝐵 = 42°,
𝑐=4
Solve the triangle. Find the m<C, and the length of sides a and b.
Find the area of the triangle ABC.
57. Given a triangle with 𝑎 = 11,
𝑏 = 14,
𝑐 = 20
Solve the triangle. Find the m<A, m<B, and m<C
𝑏=6