Math 1316 General Review for Trigonometry Last Updated 08/15/2014
Math 1316
General Review for Trigonometry
Last Updated 08/15/2014
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?
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?
7. 4x + 5y = 0, x K 0; Find csc .
a.
5 4
b.
-
5 4
c.
41 4
d.
-
4 5
Evaluate the expression. 8. sin 450? a. 0
c. 1
b.
1 2
d. Undefined
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
4. A wheel is rotating 720 times per minute.
Through how many degrees does a point on
the
edge
of
the
wheel
move
in
1 4
seconds?
a. 72? c. 1080?
b. 270? d. 810?
9. cos(-90?)
a.
3 2
c. -1
b. 0 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
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 .
a.
5 4
b.
3 4
c.
5 3
d.
4 3
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 L 0; Find sin .
a.
10 10
b.
3 10 10
c. 3
d.
1 3
11. tan , given that cot =
5 8
a.
55 8
b.
8 5
c.
5 5
d.
85 5
Use the fundamental identities to find the value of the
trigonometric function.
12.
Find tan , given that
sin =
3 4
and is in
quadrant II.
a. -
7 9
b.
-
37 7
c.
-
3 2
d.
5 4
1
13.
Find sec , given that
tan =
3 4
and is in
quadrant I.
a.
-
3 2
b.
3 7
7
c.
5 4
d. -
7 9
14. Find sec , given that tan = 0.57735027 and
is in quadrant I.
a. -1.1547005
b. -1.2559261
c. 1.2559261
d. 1.1547005
15. Find tan , given that cos = -0.58778525 and
is in quadrant II.
a. 1.9734303
b. 1.3763819
c. -1.9734303
d. -1.3763819
16. Find the exact value of x in the figure.
14
a. 5 3 c. 7 6
b. 7 3 d. 8 3
17. Find the exact value of x in the figure.
28
x
a. 14 3
c.
28 3
6
b.
28 3
3
d. 14 6
Find the exact value of the expression.
18. cos 150?
a.
3 2
b.
2 2
c. -
3 2
d. -
2 2
19. sec 210? a. - 2
c.
23 3
b. 2
d.
-
23 3
20. cos (-2190?)
a. -
3 2
c.
1 2
b.
3 2
d.
-
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.
C
A
a. 32 ft c. 30 ft
74 ft
B
b. 68 ft d. 170 ft
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
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
25. Find h as indicated in the figure. Round to the nearest foot.
24.9?
102 ft
a. 68 ft c. 65 ft
59.3?
b. 70 ft d. 62 ft
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
Find the exact value without using a calculator.
27.
csc
5 3
a. - 3
b. - 2
c.
-
1 2
d.
-
23 3
28.
sec
-5 4
a. -2
c.
-
23 3
b. - 2
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.
29.
r
=
15.95
ft;
=
29
radians
a. 3.5 ft c. 0.9 ft
b. 1.7 ft d. 5.2 ft
30. r = 116.15 in.; = 162? a. 328.4 in. c. 656.8 in.
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
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
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?
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?
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,
=
3
radians
a. 1107.9 ft2 c. 554.0 ft2
b. 50.4 ft2 d. 24.1 ft2
36. r = 19.5 mi, = 151? a. 1002.1 mi2 c. 501.1 mi2
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
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
d. 5.64 cm2
Find the exact circular function value.
39.
tan
-5 6
a. 3
b. - 3
c.
3 2
d.
3 3
40.
csc
-2 3
a.
-
1 2
c. - 2
b.
-
23 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 13
,
12 13
a.
5 12
c.
-
5 13
b.
12 13
d.
-
12 13
4
42. Find csc .
Suppose an arc of length s lies on the unit circle x2 + 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.
a.
25 24
c.
-
25 24
7 25
,
-
24 25
b.
24 7
d.
-
25 7
43. sec 0.1943 a. 0.1931 c. 0.9812
b. 0.1968 d. 1.0192
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
45. s = 7.6 a. (0.9679, 0.2513) b. (-0.2513, -0.9679) c. (-0.2513, 0.9679) d. (0.2513, 0.9679)
Find the exact values of s in the given interval that satisfy
the given condition.
46.
[0,
2);
tan2
s
=
1 3
a.
6
,
7 6
b.
3
,
2 3
,
4 3
,
5 3
c.
3
,
4 3
d.
6
,
5 6
,
7 6
,
11 6
47. [-, ); 2 cos2 s = 1
a.
4
,
4
,
4
,
7 4
b.
-
2 3
,
-
3
,
3
,
2 3
c.
-
7 4
,
-
4
,
-
4
,
-
4
d.
-
3 4
,
-
4
,
4
,
4
5
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