Download Review for Trigonometry Final

GHP Trig
Review for Trigonometry Final
Find the distance between each pair of points.
1. (4, -2) and (1, -6)
2. (-6, 3) and (-2, -5)
Sketch each angle in standard position.
3. 75º
4. 234º
Find the angle of smallest positive measure coterminal with each angle.
5. -51º
6. 792º
11
7.
4

8. 
6
Find the value of all six trigonometric functions for an angle in standard position having
each point on its terminal side. Rationalize denominators when applicable.
9. (1, -5)
10. (-3, -4)
Identify the quadrant(s) for the angle satisfying the given conditions.
11. cos  0, tan   0
12. sin   0, cos   0
Use reference angles to express the following as a function of a positive acute angle.
13. sin 330º
14. tan 150º
Solve each right triangle. In each case, C = 90º.
15. B = 46º, c = 30
16. a = 76, c = 86
Use a calculator to find each value.
17. csc 78º 21’
18. sin 72º 30’
19. Find  if sec  1.2638
20. Find  if cos  0.9754
Solve each problem.
21. The shadow of a vertical tower is 40.6 meters long when the angle of
elevation of the sun is 34.6º. Find the height of the tower.
22. Find the angle of elevation of the sun if a 48.6 foot flagpole casts a shadow
63.1 feet long.
23. A ship travels 50 km on a bearing of 27º, and then travels on a bearing of
117º for 140 km. Find the distance traveled from the starting point to the
ending point.
24. A ship leaves port and sails due west for 45 miles. Then the ship turns and
sails due south for 15 miles. Find the bearing of the ship from the port.
25. Sketch a bearing of 210º.
26. Sketch a bearing of S 36º E.
Convert each degree measure to radians, and each radian measure to degrees.
27. 75º
28. 150º
4
29.
15
8
30.
5
Find the exact values of the six trigonometric functions for each angle.
31. 300º
5
32.
6
Find each function value.
1
33. csc , if cot    , with  in quadrant IV
2
34. sin  , if sec  2 with  in quadrant IV
Write each of the following in terms of its cofunction.
35. cot 73º
36. sec 39º
37. sin 42º
Find the length of each arc intercepted by a central angle  in a circle of radius r.
2
38. r = 12.3 cm,  
radians
3
39. r = 4.82 m,   60
Find the area of a sector of a circle having radius r and central angle  .
3
40. r = 52 cm,  
radians
10
41. r = 12.7 cm,   81
Find the exact value of x in the given interval that has the given trigonometric function
value.
 3 
42.  ,  , tan x  3
 2 
 
43.  ,   , csc x  2
2 
For each function, give the amplitude, period, vertical translation, and phase shift, as
applicable.
1
2
44. y = - cos x  3
4
3
x
3 

45. y   cot  

2 4 
Graph the following functions.
1
46. 3sin x
2
47. 2cos3x
Simplify the following expressions.
cos x sin x

48.
sec x csc x
49. cos x(sec x  csc x)
Verify that each equation is an identity.
1  cos 2
 cot 
50.
sin 2
51.
cos2 x (tan2x + 1) = 1
52. sin 2
x tan x  sin x

2
2 tan x
53. sin2 x + tan2 x + cos2x = sec2x
Determine in which quadrants the solution for each of the following is found.

1  cos
54. sin  
2
2
55. cos

2

1  cos
2
Rewrite each of the following using sum and difference identities.
56. cos105
57. sin165
Find each of the following.

1

58. cos , given cos   with 0   
2
4
2


59. sin , given tan  2 with 0   
2
2
7

60. tan , given tan  
with 180    270
2
3
Find the remaining sides and angles of oblique triangle ABC.
61.
B = 42.88, C = 102.40, b = 3974 ft.
62.
C = 45.6, b = 8.94 m, a = 7.23m
63.
a = 28 ft, b = 47 ft, c = 58 ft
Find each of the following.
64.
65.
3
with θ terminating in quadrant III
4
12
sin 2θ , cos 2θ and tan 2θ, given cos θ = and sin θ > 0
13
sin θ and tan θ, given cos 2θ =