Download Math 1316 General Review for Trigonometry

Math 1316
General Review for Trigonometry
7. 4x + 5y = 0, x
5
a.
4
MULTIPLE CHOICE. Choose the one alternative that best
completes the statement or answers the question.
Find the measure of each angle in the problem.
1. Supplementary angles with measures 3x + 8
and 2x - 3 degrees
a. 83° and 97°
b. 98° and 82°
c. 128° and 52°
d. 113° and 67°
5
4
d. -
4
5
1
2
a. 0
b.
c. 1
d. Undefined
9. cos(-90°)
3
a.
2
b. 0
c. -1
d. Undefined
Use the appropriate identity to find the indicated function
value. Rationalize the denominator, if applicable. If the
given value is a decimal, round your answer to three
decimal places.
10. cot , given that tan = 0.3474
a. 2.879
b. 2.872
c. 2.893
d. 2.886
4. A wheel is rotating 720 times per minute.
Through how many degrees does a point on
1
the edge of the wheel move in seconds?
4
b. 270°
d. 810°
Suppose that is in standard position and the given point
is on the terminal side of . Give the exact value of the
indicated trig function for .
5. (18, 24); Find csc .
5
3
5
4
a.
b.
c.
d.
4
4
3
3
11. tan , given that cot
An equation of the terminal side of an angle in standard
position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a
calculator.
6. -3x + y = 0, x 0; Find sin .
10
3 10
a.
b.
10
10
d.
b. -
Evaluate the expression.
8. sin 450°
3. A wheel makes 396 revolutions per minute.
How many revolutions does it make per
second?
a. 13.2 revolutions per second
b. 2376 revolutions per second
c. 3.96 revolutions per second
d. 6.6 revolutions per second
c. 3
0; Find csc .
41
4
c.
2. Complementary angles with measures 4x and
5x - 9 degrees
a. 84° and 96°
b. 44° and 46°
c. 11° and 79°
d. 46° and 44°
a. 72°
c. 1080°
Last Updated 08/15/2014
=
5
8
a.
5 5
8
b.
8
5
c.
5
5
d.
8 5
5
Use the fundamental identities to find the value of the
trigonometric function.
3
12. Find tan , given that sin = and is in
4
quadrant II.
7
a. 9
1
3
c. -
1
3
2
b. d.
5
4
3 7
7
13. Find sec , given that tan
quadrant I.
3
a. 2
c.
5
4
14. Find sec , given that tan
is in quadrant I.
a. -1.1547005
c. 1.2559261
15. Find tan , given that cos
is in quadrant II.
a. 1.9734303
c. -1.9734303
=
3
and
4
b.
17. Find the exact value of x in the figure.
is in
3 7
7
d. -
7
9
28
= 0.57735027 and
x
b. -1.2559261
d. 1.1547005
a. 14 3
= -0.58778525 and
c.
b. 1.3763819
d. -1.3763819
28 6
3
b.
28 3
3
d. 14 6
Find the exact value of the expression.
18. cos 150°
3
a.
b.
2
16. Find the exact value of x in the figure.
c. -
14
3
2
d. -
2
2
2
2
19. sec 210°
a. -
a. 5 3
c. 7 6
c.
b. 7 3
d. 8 3
2
2 3
3
20. cos (-2190°)
3
a. 2
c.
1
2
b.
2
d. -
2 3
3
b.
d. -
3
2
1
2
Solve the problem.
21. On a sunny day, a flag pole and its shadow
form the sides of a right triangle. If the
hypotenuse is 40 meters long and the shadow
is 32 meters, how tall is the flag pole?
a. 72 m
b. 64 m
c. 51 m
d. 24 m
2
22. To measure the width of a river, a surveyor
starts at point A on one bank and walks 74 feet
down the river to point B. He then measures
the angle ABC to be 23°32'12''. Estimate the
width of the river to the nearest foot. See the
figure below.
26. The angle of elevation from a point on the
ground to the top of a tower is 38° 19 . The
angle of elevation from a point 145 feet farther
back from the tower is 26° 41 . Find the height
of the tower. Round to the nearest foot.
a. 2002 ft
b. 196 ft
c. 211 ft
d. 200 ft
C
Find the exact value without using a calculator.
5
27. csc
3
a. - 3
c. A
74 ft
a. 32 ft
c. 30 ft
B
b. 68 ft
d. 170 ft
28. sec
b. - 2
1
2
d. -
-5
4
b. - 2
a. -2
23. An airplane travels at 180 km/h for 5 hr in a
direction of 289° from Greenville. At the end
of this time, how far west of Greenville is the
plane (to the nearest kilometer)?
a. 310 km
b. 952 km
c. 293 km
d. 851 km
2 3
3
c. -
2 3
3
d.
2
2
Find the length of an arc intercepted by a central angle
in a circle of radius r. Round your answer to 1 decimal
place.
24. A ship travels 99 km on a bearing of 35°, and
then travels on a bearing of 125° for 129 km.
Find the distance from the starting point to the
end of the trip, to the nearest kilometer.
a. 81 km
b. 57 km
c. 163 km
d. 228 km
29. r = 15.95 ft;
=
29
radians
a. 3.5 ft
c. 0.9 ft
30. r = 116.15 in.; = 162°
a. 328.4 in.
c. 656.8 in.
25. Find h as indicated in the figure. Round to the
nearest foot.
b. 1.7 ft
d. 5.2 ft
b. 164.2 in.
d. 104.5 in.
31. Find the distance between City E, 43° N and
City F, 74° S. (Round to the nearest kilometer.)
a. 3455 km
b. 13,069 km
c. 13,077 km
d. 3463 km
24.9°
Assume that the cities lie on the same north-south line
and that the radius of the earth is 6400 km.
32. Find the latitude of Winnipeg, Canada if
Winnipeg and Austin, TX, 30°N, are 2234 km
apart.
a. 20°N
b. 70°N
c. 50°N
d. 60°N
59.3°
102 ft
a. 68 ft
c. 65 ft
b. 70 ft
d. 62 ft
3
33. A wheel with a 38-inch radius is marked at
two points on the rim. The distance between
the marks along the wheel is found to be 14
inches. What is the angle (to the nearest tenth
of a degree) between the radii to the two
marks?
a. 19.1°
b. 23.1°
c. 17.1°
d. 21.1°
Find the exact circular function value.
-5
39. tan
6
34. Two wheels are rotating in such a way that the
rotation of the smaller wheel causes the larger
wheel to rotate. The radius of the smaller
wheel is 3.1 centimeters and the radius of the
larger wheel is 17.4 centimeters. Through how
many degrees (to the nearest hundredth of a
degree) will the larger wheel rotate if the
smaller one rotates 140°?
a. 24.94°
b. 25.94°
c. 26.94°
d. 24.84°
40. csc
=
3
c.
3
2
= 151°
a. 1002.1 mi2
c. 501.1 mi2
3
3
d.
-2
3
1
2
2
c. -
b. -
2 3
3
d. -
3
The figure shows an angle in standard position with its
terminal side intersecting the unit circle. Evaluate the
indicated circular function value of .
41. Find sin .
-
5 12
,
13 13
b. 50.4 ft2
d. 24.1 ft2
b. 25.7 mi2
d. 33.9 mi2
37. Find the measure (in radians) of a central angle
of a sector of area 46 square inches in a circle of
radius 7 inches. Round to the nearest
hundredth.
a. 2.82 radians
b. 0.94 radians
c. 3.76 radians
d. 1.88 radians
a.
38. A pendulum swings through an angle of 19°
each second. If the pendulum is 17 cm in
length and the complete swing from right to
left lasts 2 seconds, what area is covered by
each complete swing? Round to the nearest
hundredth.
a. 47.92 cm2
b. 191.67 cm2
c. 95.84 cm2
3
b. -
radians
a. 1107.9 ft2
c. 554.0 ft2
36. r = 19.5 mi,
3
a. -
Find the area of a sector of a circle having radius r and
central angle . If necessary, express the answer to the
nearest tenth.
35. r = 23.0 ft,
a.
5
12
c. -
d. 5.64 cm2
4
5
13
b.
12
13
d. -
12
13
42. Find csc .
Suppose an arc of length s lies on the unit circle x 2 + y2 =
1, starting at point (1, 0) and terminating at the point (x, y).
Use a calculator to find the approximate coordinates (x, y).
Round coordinates to four decimal places when
appropriate.
7
24
,25
25
a.
25
24
c. -
25
24
43. sec 0.1943
a. 0.1931
c. 0.9812
b.
24
7
d. -
45. s = 7.6
a. (0.9679, 0.2513)
b. (-0.2513, -0.9679)
c. (-0.2513, 0.9679)
d. (0.2513, 0.9679)
25
7
b. 0.1968
d. 1.0192
Find the exact values of s in the given interval that satisfy
the given condition.
1
46. [0, 2 ); tan2 s =
3
Use a table or a calculator to evaluate the function. Round
to four decimal places.
44. csc 0.2391
a. 0.2368
b. 0.9716
c. 4.2225
d. 1.0293
a.
b.
c.
d.
7
6 6
,
3
3
6
,
2 4
5
,
,
3 3
3
,
4
3
,
5 7
11
,
,
6 6
6
47. [- , ); 2 cos2 s = 1
7
,
,
a. ,
4 4 4 4
5
b. -
2
2
,- , ,
3
3 3 3
c. -
7
,,,4
4
4
4
d. -
3
,- , ,
4
4 4 4
48. Let angle POQ be designated . Angles PQR
and VRQ are right angles. If = 45°, find the
exact length of OQ.
a.
2
c. 0
50. Let angle POQ be designated . Angles PQR
and VRQ are right angles. If = 27°, find the
length of OU accurate to four decimal places.
a. 2.2027
c. 1.1223
b. 1
d.
2
2
51.
49. Let angle POQ be designated . Angles PQR
and VRQ are right angles. If = 80°, find the
length of OQ accurate to four decimal places.
=
radian per min, t = 13 min
6
a.
c.
b. 0.8910
d. 0.4540
78
78
Use the formula
radians
b.
13
6
radian
d.
6
radians
13
=
t
radians
to find the value of the missing
variable. Give an exact answer unless otherwise indicated.
52. = 9.2302 radians per min, = 13.09 radians
(Round to four decimal places when
necessary.)
a. 1.4182 min
b. 0.7051 min
c. 22.3202 min
d. 120.8233 min
a. 0.1736
c. 5.7588
Use the formula v = r to find the value of the missing
variable. Give an exact answer unless otherwise indicated.
53. v = 16 ft per sec, r = 3.3 ft (Round to four
decimal places when necessary.)
a. 0.952 radian per sec
b. 5.0929 radians per sec
c. 0.2063 radian per sec
d. 4.8485 radians per sec
b. 0.9848
d. 5.6713
6
a.
Use the formula s = r t to find the value of the missing
variable. Give an exact answer.
54. s =
3
a.
m, r = 7 m, t = 32 sec
672
radian per sec
b. 672 radians per sec
21
radians per sec
c.
32
d.
32
radian per sec
21
55. A wheel is rotating at 8 radians/sec, and the
wheel has a 38-inch diameter. To the nearest
foot, what is the speed of a point on the rim in
ft/min?
a. 755 ft/min
b. 765 ft/min
c. 760 ft/min
d. 750 ft/min
b.
56. A wheel with a 22-inch diameter is turning at
the rate of 58 revolutions per minute. To the
nearest inch, what is the speed of a point on
the rim in in./min?
a. 4055 in./min
b. 4009 in./min
c. 4062 in./min
d. 4016 in./min
Graph the function.
1
57. y = sin x
4
c.
7
d.
b.
c.
58. y = cos
1
x
3
d.
a.
8
59. y = 2 + sin x +
d.
3
a.
Graph the function over a one-period interval.
60. y = 4 + 4 sin(x - )
b.
a.
c.
9
b.
+ tan )2 =
63. (sec
1 + sin
1 - sin
MULTIPLE CHOICE. Choose the one alternative that best
completes the statement or answers the question.
Use Identities to find the exact value.
64. cos (-75°)
c.
a.
2-
6
c.
24
6
64
b.
2
d. - 6 -
2
65. cos 255°
66. cos
a.
6-
2
c.
64
2
a.
24
6
c.
6+
4
2
b.
2-
6
d.
24
6
b.
- 64
d.
64
12
d.
2
1
, with s in
3
67. Find cos(s + t) given that cos s =
quadrant I, and sin t = -
2
1
, with t in quadrant
2
IV.
3+2 2
6
a.
c.
2 6-1
6
3-2 2
6
b.
d.
2 6+1
6
68. Find cos(s - t) given that cos s = SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
quadrant II, and cos t =
Verify that each equation is an identity.
cos
61. sec + tan =
1 - sin
quadrant IV.
56
a.
65
62.
c. -
sec - 1
tan
=
tan
sec + 1
10
56
65
4
, with s in
5
5
, with t in
13
b.
16
65
d. -
16
65
69. sin 15°
6+
4
a.
c.
-
2
64
71. sin
b.
2
70. tan 75°
a. - 3 - 2
c. - 3 + 2
64
d.
6+
4
-
Find the exact value of the expression using the provided
information.
1
76. Find sin(s - t) given that cos s = , with s in
3
2
2
quadrant I, and sin t = quadrant IV.
3+2 2
a.
6
3-2
3+2
b.
d.
c.
11
12
a.
6+
4
2
c.
64
2
b.
d.
-
64
2
-
6+
4
2
a.
6
c.
64
2
73. tan 345°
a. 3 + 2
c. - 3 - 2
75. tan
a.
2
b.
d.
2+2 6
4
c. -
6
c.
64
2
3
3
171
221
b.
21
221
d.
171
221
24
25
b.
c.
7
25
d. -
=-
a. -
1
d.
2
b. 2 d. 2 +
5
, with s in
13
15
, with t in
17
a.
79. sin
3+1
2
c.
11
12
a. -2 c. -2 +
2 6+1
6
Use identities to find the indicated value for each angle
measure.
3
Find cos(2 ).
78. sin = , cos > 0
5
b. - 3 + 2
d. 3 - 2
b.
d.
quadrant II, and sin t =
Use a sum or difference identity to find the exact value.
7
74. sin
12
6+
4
2 6-1
6
quadrant II.
21
a. 221
2+
4
3-2 2
6
b.
77. Find sin(s + t) given that cos s = -
7
72. sin
12
24
1
, with t in
2
4
,
5
2
7
25
<
1
5
<2
Find cos(2 ).
b. -
24
25
7
25
d.
24
25
7
25
Find the exact value by using a half-angle identity.
80. sin 22.5°
1
1
2+ 2
2- 2
a. b.
2
2
3
3
c.
11
1
2
2+
2
d. -
1
2
2-
2
81. cos 75°
1
a.
2
c. -
21
2
82. tan 75°
a. -2 c. -2 +
83. sin
84. cos
1
b. 2
3
2-
3
d.
2+
1
2
2+
88. 2 sin2 x = sin x
2
,
a.
3 3
3
3
b.
c.
3
3
b. 2 d. 2 +
3
3
a. -
1
2
2+
3
b.
1
2
2+
3
c. -
1
2
2-
3
d.
1
2
2-
3
a.
b.
a. -
1
2
2+
3
b.
1
2
2-
3
c.
c. -
1
2
2-
3
d.
1
2
2+
3
d.
b. -2 - 3
d. 2 - 3
a.
2 3+2
5
b.
4 3-3
10
c.
-25 3-48
100
d.
4 3+3
10
3
2
, ,
2 3 3
6
,
b.
d.
6
2
6
6
+ 2n ,
5
+ 2n
6
+ 2n ,
5
3
+ 2n ,
+ 2n
6
2
+ 2n ,
3
+ 2n
2
+ 2n ,
5
3
+ 2n ,
+ 2n
6
2
a.
2
7 7
13 5 19
,
,
,
,
,
12 6 3 12 6
12 3 12
,
b. {0}
3
2 2
,
=1
Solve the equation for solutions in the interval [0, 2 ).
3
91. sin 4x =
2
c.
,
4
5
6
a. {51.8° + 360°n, 128.2° + 360°n}
b. {70.5° + 360°n, 180° + 360°n, 289.5° +
360°n}
c. {49.8° + 360°n, 130.2° + 360°n, 229.8° +
360°n, 310.2° + 360°n}
d. {103.2° + 360°n, 145.2° + 360°n, 283.2° +
360°n, 325.2° + 360°n}
Solve the equation for exact solutions over the interval [0,
2 ).
87. cos2 x + 2 cos x + 1 = 0
c. {2 }
,
90. 3 cos2 + 2 cos
Give the exact value of the expression.
3
3
86. cos arcsin + arccos
5
2
}
5
6
Solve the equation (x in radians and in degrees) for all
exact solutions where appropriate. Round approximate
answers in radians to four decimal places and approximate
answers in degrees to the nearest tenth.
89. 2 sin2 x + sin x = 1
5
12
a.
2
,
d. 0, ,
5
12
85. tan 165°
a. 2 + 3
c. -2 + 3
6
7
4
4
d. 0,
12
,
,
5
4
4
,
92. cos 2x =
a.
98. sin-1 x + tan-1 x = 0
3
3
,
a. 4
4
2 - cos 2x
b.
3 5
7
,
,
4 4 4
4
c.
9 7
15
,
,
,
8 8 8
8
,
d. 0,
c. -
2
4
, ,
3
3
100. A = 37°10'
B = 26°10'
a = 36.2
a. C = 117°40', b = 53.5, c = 26.4
b. C = 117°40', b = 26.4, c = 53.5
c. C = 116°40', b = 26.4, c = 53.5
d. C = 116°40', b = 53.5, c = 26.4
Solve the equation for solutions over the interval [0, 2 ).
Write solutions as exact values or to four decimal places,
as appropriate.
x
x
94. sin + cos = 2
2
2
b.
c.
d.
4
95. tan 2x + sec 2x = 2
a. {0.6435, 6.9267}
c. {1.1072, 4.2488}
}
Find the area of triangle ABC with the given parts. Round
to the nearest tenth when necessary.
101. A = 38.2°
b = 14.2 in.
c = 4.4 in.
a. 26.6 in.2
b. 24.6 in.2
2
b. {2.2143, 8.4975}
d. {0.3218, 3.4634}
c. 17.3 in.2
Solve the equation for exact solutions.
96. arcsin 2x + 2 arccos x =
102. A = 25°50'
b = 17.5 m
c = 8.9 m
3
3
,
2
2
a. 1
b. -
c. 0
3
3
,
d. 4
4
a. 67.8 m2
c. 17 m2
c. -
b. 3
3
,
4
4
d. 19.3 in.2
b. 33.9 m2
d. 69.8 m2
Solve the problem.
103. Two tracking stations are on the equator 173
miles apart. A weather balloon is located on a
bearing of N 42°E from the western station and
a bearing of N 12°E from the eastern station.
How far, to the nearest mile, is the balloon
from the western station? Round to the nearest
mile.
a. 271 mi
b. 280 mi
c. 338 mi
d. 347 mi
97. arcsin x + 2 arctan x =
a. 0
d. 1
Solve the triangle. Round to the nearest tenth when
necessary or to the nearest minute as appropriate.
99. B = 40.9°
C = 114.5°
b = 17.8
a. A = 22.6°, a = 26.7, c = 13.3
b. A = 24.6°, a = 13.3, c = 26.7
c. A = 22.6°, a = 24.7, c = 11.3
d. A = 24.6°, a = 11.3, c = 24.7
Solve the equation for solutions in the interval [0°, 360°).
Round to the nearest degree.
93. sin 2 = cos
a. {15°, 165°, 195°, 345°}
b. {30°, 90°, 150°, 270°}
c. {0°, 120°, 180°, 240°}
d. {105°, 165°, 285°, 345°}
a. {0 , }
3
3
,
2
2
b. 0
3
3
,
2
2
d. 1
13
104. An airplane is sighted at the same time by two
ground observers who are 2 miles apart and
both directly west of the airplane. They report
the angles of elevation as 13° and 20°. How
high is the airplane? Round to the nearest
hundredth of a mile.
a. 1.92 mi
b. 1.26 mi
c. 0.68 mi
d. 0.45 mi
108. C = 118.5°
a = 7.3 m
b = 11.7 m
a. c = 22.3 m, A = 20.8°, B = 40.7°
b. c = 16.5 m, A = 22.8°, B = 38.7°
c. No triangle satisfies the given conditions.
d. c = 19.4 m, A = 24.8°, B = 36.7°
109. a = 18.9 cm
b = 15.7 cm
c = 14.9 cm
Find the missing parts of the triangle.
105. B = 19.7°
b = 12.80
a = 18.99
If necessary, round angles to the nearest tenth
and side lengths to the nearest hundredth.
a. A1 = 30.01°, C1 = 130.29°, c1 = 28.96;
a. 123 cm2
c. 114 cm2
b. 117 cm2
d. 120 cm2
110. Two ships leave a harbor together traveling on
courses that have an angle of 129° between
them. If they each travel 502 miles, how far
apart are they (to the nearest mile)?
a. 1812 mi
b. 432 mi
c. 40 mi
d. 906 mi
A2 = 149.99°, C2 = 10.31°, c2 = 6.8
b. A = 149.99°, C = 10.31°, c = 6.8
c. no such triangle
d. A = 30.01°, C = 130.29°, c = 28.96
106. C = 35°30'
a = 18.76
c = 16.15
If necessary, round side lengths to the nearest
hundredth.
a. A1 = 42°25', B1 = 102°05', b1 = 27.2;
111. Two airplanes leave an airport at the same
time, one going northwest (bearing 135°) at 417
mph and the other going east at 338 mph.
How far apart are the planes after 4 hours (to
the nearest mile)?
a. 2193 mi
b. 2793 mi
c. 698 mi
d. 2325 mi
A2 = 137°35', B2 = 6°55', b2 = 3.35
b. A = 42°25', B = 102°05', b = 25.19
c. no such triangle
d. A1 = 102°05', B1 = 42°25', b1 = 17.52;
Find the magnitude and direction angle (to the nearest
tenth) for each vector. Give the measure of the direction
angle as an angle in [0,360°].
112. 2, 2
a. 2 2; 45°
b. 2 2; 225°
c. 2; 225°
d. 4; 45°
A2 = 6°55', B2 = 137°35', b2 = 26.19
Find the missing parts of the triangle. Round to the
nearest tenth when necessary or to the nearest minute as
appropriate.
107. C = 106.2°
a = 6.3 km
b = 8.1 km
a. c = 11.6 km, A = 31.4°, B = 42.4°
b. c = 17.4 km, A = 29.4°, B = 44.4°
c. c = 14.5 km, A = 33.4°, B = 40.4°
d. No triangle satisfies the given conditions.
113. -6 2, -6 2
a. 12 2; 135°
c. 12; 45°
b. 12; 225°
d. 24; 45°
Two forces act at a point in the plane. The angle between
the two forces is given. Find the magnitude of the
resultant force.
114. forces of 28.1 and 43.2 lb, forming an angle of
76.5°
(round to the nearest pound)
a. 2089 lb
b. 46 lb
c. 57 lb
d. 71 lb
14
Find the dot product for the pair of vectors.
115. 10, -12 , -8, -4
a. 48
b. -32
c. -80
d. -128
116. 5i - 4j, 8i + j
a. 36
c. 44
Find the product. Write the product in rectangular form,
using exact values.
124. [4(cos 30° + i sin 30°)] [6(cos 330° + i sin 330°)]
a. 12 3 + 12i
b. -12 + 12 3i
c. 24
d. 24i
b. -27
d. 0
Find the quotient and write in rectangular form. First
convert the numerator and denominator to trigonometric
form.
5(cos 200° + i sin 200°)
125.
4(cos 50° + i sin 50°)
Find the angle between the pair of vectors to the nearest
tenth of a degree.
117. 3, 7 , 9, -6
a. 40.3°
b. 50.3°
c. 100.5°
d. 110.5°
118. 9i - 5j, 2i - 9j
a. 114.4°
c. 44.7°
b. 48.4°
d. 126.9°
126.
5 3 5
+ i
8
8
b. -2 + 2 3i
c. -
1
3
i
+
2
2
d. -10 + 10 3i
8(cos 90 + i sin 90)
3(cos 30 + i sin 30)
Determine whether the pair of vectors is orthogonal.
119. -2, 6 , -8, -5
a. Yes
b. No
120. 3i - 2j, -8i - 12j
a. Yes
a. -
a. 8 + 8 3i
c.
b. No
4 4 3
i
+
3
3
b. 1 +
d.
3i
5 5 3
i
+
2
2
Find the given power. Write answer in rectangular form.
127. (- 3 + i)6
121. Two forces of 498 newtons and 257 newtons
act at a point. The resultant force is 578
newtons. Find the angle between the forces.
a. 85.5°
b. 80.3°
c. 94.5°
d. 164.0°
a. 64i
c. -64 3 + 64i
128. -
122. A force of 621 lb is required to pull a boat up a
ramp inclined at 19° with the horizontal. How
much does the boat weigh?
a. 2494 lb
b. 587 lb
c. 1907 lb
d. 602 lb
1
3 10
i
2
2
a.
1
3
i
+
2
2
c. -
123. Two boats are pulling a disabled vessel toward
the landing dock with forces of 950 lb and 940
lb. The angle between the forces is 21.8°. Find
the direction and magnitude of the equilibrant.
a. 1856 lb at an angle of 10.8° with the
950-lb force
b. 1856 lb at an angle of 79.2° with the
940-lb force
c. 186 lb at an angle of 169.2° with the
950-lb force
d. 1856 lb at an angle of 169.2° with the
950-lb force
b. 64 - 64 3i
d. -64
1
3
i
+
2
2
b.
d. -
Find all specified roots.
129. Cube roots of 1.
1
3
1
3
i, - +
i
a. 1, +
2
2
2
2
b. 1, c. 1,
1
3
1
3
i, - i
+
2
2
2
2
1
3
1
3
i, - i
2
2
2
2
d. -1, 1
15
1
3
i
2
2
1
3
i
2
2
130. Cube roots of i.
3 1
3 1
+ i, + i, i
a.
2
2
2
2
b.
3 1
3 1
- i, - i, i
2
2
2
2
c.
3 1
3 1
- i, - i, -i
2
2
2
2
d.
3 1
3 1
+ i, + i, -i
2
2
2
2
16
Answer Key
Testname: GENERAL TRIG REVIEW
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
d
b
d
c
a
b
c
c
b
a
d
b
c
d
d
b
c
c
d
b
d
a
d
c
c
d
d
b
b
a
b
c
d
a
c
c
d
c
d
b
b
c
d
c
d
d
d
d
a
a
17
Answer Key
Testname: GENERAL TRIG REVIEW
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
b
a
d
a
c
b
b
b
a
b
61. sec
62.
+ tan
=
1
cos
+
sin
cos
sec - 1 sec - 1 sec
=
·
tan
tan
sec
63. (sec
=
1 + sin
cos
=
1 + sin
cos
·
1 - sin
1 - sin
+1
sec2 - 1
tan2
=
=
+ 1 tan (sec + 1) tan (sec
+ tan )2 = sec2 + 2 sec
tan
+ tan2 =
1
cos2
+
(1 + sin )2
1 + sin
=
(1 - sin )(1 + sin ) 1 - sin
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
=
b
d
c
a
c
b
d
c
b
d
a
c
d
c
c
a
b
a
d
b
b
c
b
a
d
d
b
a
c
b
18
2 sin
cos2
1 - sin2
cos2
cos
=
=
cos (1 - sin ) cos (1 - sin )
1 - sin
+ 1)
+
=
tan
sec + 1
sin2
cos2
=
1 + 2 sin
cos2
+ sin2
=
(1 + sin )2
=
1 - sin2
Answer Key
Testname: GENERAL TRIG REVIEW
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
d
d
c
d
b
d
c
d
b
c
b
a
a
a
b
c
d
b
a
b
c
b
a
c
b
b
a
a
c
d
c
a
c
d
d
b
d
19