Review 10/1-4
Find the values of the six trigonometric functions for θ.
1.
2.
3.
θ
40
41
9
25
24
6
θ
7
2
7
Use a trigonometric function to find the value of x.
5.
6.
7.
45°
x
6
x
5
4.
θ
4
8.
30°
7
x
45°
60°
8
x
9. A biologist’s eye level is 5.5 ft above the ground. She measures the angle of elevation to an eagle’s
nest on a cliff to be 66° when she stands 50 ft from the cliff’s base. To the nearest foot, what is the
height of the eagle’s nest?
10. The angle of depression from a watchtower to a forest fire is 8°. If the watchtower is 25 meters
high, what is the distance between the base of the tower and the fire to the nearest meter?
Draw an angle with the given measure in standard position.
11. -270°
12. 405°
13. -55°
14. 380°
Point P is a point on the terminal side of θ in standard position. Find the exact value of the six
trigonometric functions for θ.
15. P(12, -5)
16. P(-2, 7)
17. P(-6, 8)
18. P(-3, -8)
Convert each measure from degrees to radians or from radians to degrees.
3π
10π
19. -120°
20. 63°
21.
22. 
8
3
3π
4π
23. 300°
24. -55°
25.
26. 
10
15
Use the unit circle to find the exact value of each trigonometric function.
π
π
27. cos 210°
28. tan 120°
29. cos
30. tan
2
3
5π
5π
31. sin 120°
32. tan 135°
33. cos
34. sin
4
6
35. A bicycle tire rotates through an angle of 3.4π radians in 1 second. If the radius of the tire is 0.34
meters, how far does the bicycle travel each second? Round your answer to the nearest tenth.
36. The minute hand on a clock on a town hall tower is 1.5 meters in length.
a. Find the angle in radians through which the minute hand rotates in 10 minutes.
b. To the nearest tenth of a meter, how far does the tip of the minute hand travel in 10
minutes?
Evaluate each inverse trigonometric function. Give your answer in both radians and degrees.


3
1
2
3
-1 


37. Sin-1
38. Tan-1  
39.
Cos
40. Sin-1




2
2
 2 
 3 
41. A driver uses a ramp when unloading supplies from his truck. The ramp is 10 feet long, and the bed
of the truck is 4 feet off the ground. To the nearest degree, what angle does the ramp make with
the ground?
42. A skateboard ramp is 39 inches long and rises to a height of 22 inches. To the nearest degree,
what angle does the ramp make with the ground?
Answers:
1. sin θ = 9/40
cos θ = 40/41
tan θ = 9/40
csc θ = 40/9
sec θ = 41/40
cot θ = 40/9
5. x = 5 2
9. 118 feet
11.
2. sin θ = 24/25
cos θ = 7/25
tan θ = 24/7
csc θ = 25/24
sec θ = 25/7
cot θ = 7/24 `
6. x = 3 2
10. 178 meters
12.
3. sin θ = 15 /5
cos θ = 10 /5
tan θ = 6 /2
csc θ = 15 /3
sec θ = 10 /2
cot θ = 6 /3
7. x = 7 3 /3
4. sin θ = 4 23 /23
cos θ = 161 /23
tan θ = 4 7 /7
csc θ = 23 /4
sec θ = 161 /7
cot θ = 7 /4
8. x = 16
13.
14.
15. sin θ = -5/13
cos θ = 12/13
tan θ = -5/12
csc θ = -13/5
sec θ = 13/12
cot θ = -12/5
19. -2π/2
23. 5π/3
27. - 3 /2
31. 3 /2
35. 3.7 meters
37. 60°, π/3
41. 24°
16. sin θ = 7 53 /53
17. sin θ = 4/5
cos θ = -2 53 /53
cos θ = -3/5
tan θ = -7/2
tan θ = -4/3
csc θ = 53 /7
csc θ = 5/4
sec θ = - 53 /2
sec θ = -5/3
cot θ = -2/7
cot θ = -3/4
20. 7π/20
21. 67.5°
22.
24. -11π/36
25. 54°
26.
28. - 3
29. 0
30.
32. -1
33. - 2 /2
34.
36. a. π/3 radians b. 1.6 meters
38. -30°, -π/6
39. 135°, 3π/4
40.
42. 34°
18. sin θ = -8 73 /73
cos θ = -3 73 /73
tan θ =8/3
csc θ = - 73 /8
sec θ = - 73 /3
cot θ = 3/8
-600°
-48°
3
½
30°, π/6