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MATH 1112 Trigonometry
Final Exam Review
1. Convert 105° to exact radian measure.
2. Convert 2° to radian measure to the nearest hundredth of a radian.
3. Find the length of the arc that subtends an central angle of 150° on a circle if radius 5cm.
4. Find the equivalent number of radians in revolution.
5. A wheel is rotating at 100 revolutions per second. Find the angular velocity in radians per
second.
6. Find the area of a sector of a circle with a radius of 10 centimeters and a central angle of 120°.
Round to the nearest hundredth of a square centimeter, and use the key.
12
7. Find the area of the shaded region to the right. Round to the nearest
50°
hundredth.
8. If
is an acute angle in standard position and
9. Find the exact value of
, find
.
.
10. Find the value of the six trigonometric functions of the angle in
standard position with the terminal side passing through the point
(
).
√
11. Given that
for an angle in quadrant IV, find the exact value of
( 0 ). Round to four decimal places.
12. Use a calculator to evaluate
13. Evaluate
.
14. State the amplitude and period of the graph of ( )
15. State the period of the function ( )
2
16. Sketch the graph of ( )
).
2
(
.
.
17. Sketch the graph of ( )
2 .
18. List the minimum point(s) for the graph of ( )
with 0
19. Find the phase shift and period for the function ( )
20. Sketch the graph of ( ) 2
21. Write
2
2
22. Given
.
with
2 .
(
).
.
in terms of a single trigonometric function.
in quadrant II and
with
in quadrant IV, find
(
).
23. Write
in terms of a single trigonometric function.
24. Use a half-angle identity to evaluate
22 5°.
25. Find the exact value of
2 given
26. Sketch the graph of ( )
27. Write 2
and
is in quadrant I.
.
in terms of a single trigonometric function.
28. Find the exact value of
.
Revised Spring 2013
29. Find the approximate radian value for
30. Find the approximate degree value for
31. Evaluate
32. Solve for :
(
( 0 2 15).
0 25 .
).
(
).
33. Solve the equation 2
1 0 0°
0°. Round to the nearest tenth.
34. Solve the equation 5
0, 0°
0°. Round to the nearest tenth.
35. Find the measure of angle of a right triangle if
25cm and
1 cm.
36. Solve triangle
if
°,
°, and
52in.
37. Find in triangle
if
2 m,
m, and
°.
38. In triangle
,
110°,
10km, and
20km. Find side .
39. In triangle
,
21ft,
1 ft, and
25ft. Find angle .
40. Given angle measures 1°, side measures 10 yards, and side measures 6 yards, find the
area o triangle
. Round to the nearest square yard.
41. Given
2 m,
2 m, and
0m, find the area of triangle
. Round to the nearest
square meter.
42. Find | | if
5
.
43. Write
1 √ in polar form.
(
44. Write
0°
0°) in standard
form.
45. A vector has a magnitude of 12 and a direction of 0°. Write its horizontal and vertical
components. Round to the nearest tenth.
46. Find the product of 2(
55°
55°) and (
1 5°
1 5°).
47. Complete the identity
.
) and terminal point (5 ).
48. Find the position vector of a vector with initial point ( 2
49. From the top of a cliff 1,300 feet above sea level, the angle of depression to a ship is 15°. What
is the distance from the top of the cliff to the ship? Round to the nearest foot.
50. The measure of the angle of elevation from a position 65 feet from the base to the top of a
flagpole is 2°. Find the height of the flagpole to the nearest tenth of a foot.
51. A boat travels at 55 miles per hours for 1 hour at a bearing of 15°. The boat then travels at 50
miles per hour for 2 hours at a bearing of 225°. At the end of these 3 hours, how far is the boat
from the starting point? Round to the nearest mile.
52. To find the distance across a canyon, a surveying team locates points and on one side of
the canyon and point on the other side of the canyon. The distance between and is found
to be 92 yards. The angle
is 67° and angle
is 89°. Find the distance across the
canyon. Round to the nearest yard.
53. From a certain port, a ship travels 80 miles east and then turns 90° and travels 65 miles to the
south. Find the bearing and distance of the ship from port. Round to the nearest tenth.
54. A belt traveling at a rate of 25 feet per second drives a pulley at a speed of 800 revolutions per
minute. Find the radius of the pulley to the nearest hundredth of an inch.
55. A car is traveling 55 miles per hour. If the radius of the wheel is 11 inches, find the angular
velocity in revolutions per minute.
Revised Spring 2013
56. Solve for
57. Solve for
58. Convert (
over the interval 0
over the interval 0
2 :
2 :(
.
2)(
1)
0.
), given in polar coordinates, to rectangular coordinates.
59. Convert (2 2), given in rectangular coordinates, to polar coordinates.
60. Find the measure of the angle between vectors
and
2
5.
Revised Spring 2013
Answers
17. -axis is scaled by ,
1.
-axis is scaled by 1
2. 0.73
3.
cm
4.
5. 200
6. 104.72
7. 62.83
8.
9.
√
10.
,
,
,
,
,
√
11.
18. ( 1)
19. Phase shift = 2 ,
Period =
20. -axis is scaled by ,
-axis is scaled by 1
12. 1 2116
13.
√
14. Amplitude = 3, Period = 4
15.
16. -axis is scaled by ,
-axis is scaled by 1
21.
22.
√
23.
2
24. √2 1
25.
Revised Spring 2013
26. -axis is scaled by ,
-axis is scaled by 1
54. 5
55. 840rpm
56. 0
57.
58. ( √
59. (2√2
)
)
60. 105°
27.
28.
29. 1.8666
30.
°
31.
32.
33. 12 °, 11 2°, 1 2 °, 2 2°
34.
°, 1 1°
35. 5 °
36.
°,
52,
1
37. No solution
38. 25.2km
39. °
40. 26
41. 316
42. √
43. 2 (
)
44.
√
45.
21
11
46. 12(
2 0°
2 0°)
47.
48.
10
49. 5,023ft
50. 40.6ft
51. 114mi
52. 208yds
53. 12 1° ( 50 ° ), 103.1mi
Revised Spring 2013