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Unit 6 Trigonometry
Review Problems
PreCalculus 6-R
Review Problems
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-1
1
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Find the degree measure of the angle:
12°
Find the degree measure of the angle:
-450°
Review Problems
5
• To measure the speed of a current, scientists place a paddle
wheel in the stream and observe the rate at which it rotates. If
the paddle wheel has radius 3.2 m and rotates at 100 rpm, find
the speed of the current in m/s.
33.51
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6
• Find sin a and cos B if x = 4, and y = 1.
sin a = ,
cos =
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7
• What is the side labeled x equal to, if y = 22?
11
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• Find x correct to one decimal place.
28.9
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• The angle of elevation to the top of a particular
skyscraper in New York is found to be 12°
from the ground at a distance of 1.3 mi from
the base of the building. Using this information,
find the height of the skyscraper.
1459 ft
Review Problems
10
• A man is lying on the beach, flying a kite. He
holds the end of the kite string at ground level,
and estimates the angle of elevation of the kite
to be 55° . If the string is 470 ft long, how high is
the kite above the ground?
385 ft
Review Problems
11
• A water tower is located x = 350 ft from a building (see
the figure). From a window in the building it is
observed that the angle of elevation to the top of the
tower is 39° and the angle of depression to the bottom
of the tower is 25° . How tall is the tower (t)? How high
is the window (w)?
t = 447 ft;
w = 163 ft
Review Problems
12
• When the moon is exactly half full, the earth, moon,
and sun form a right angle (see the illustration). At that
time the angle formed by the sun, earth, and moon is
measured to be 89.75 . If the distance from the earth
to the moon is 235000 mi, estimate the distance from
the earth to the sun.
53,858,204 mi
Review Problems
13
• From a satellite 500 mi above the earth, it is observed
that the angle formed by the vertical and the line of
sight to the horizon is 60.276 . Use this information to
find the radius of the earth.
3300 mi
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• A winch of radius 3 ft is used to lift
heavy loads. If the winch makes 7
revolutions every 15 s, find the speed
at which the load is rising.
8.796
Review Problems
15
• Find the side labeled x. State your answer
correct to five decimal places.
31.40177
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• Find the side labeled x. State your answer
correct to five decimal places.
31.72546
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• Find x correct to one decimal place.
108.9
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• A 66-ft tree casts a shadow that is 110 ft long.
What is the angle of elevation of the sun?
Please give the answer to one decimal place.
31.0°
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• An airplane is flying at an elevation of 5900 ft, directly
above a straight highway. Two motorists are driving
cars on the highway on opposite sides of the plane,
and the angle of depression to one car is 52 and to
the other is 51 . How far apart are the cars? Please
round the answer to the nearest foot.
9387 ft
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• Evaluate the expression without using a calculator.
0
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•
•
•
•
Solve the right triangle.
(a) Find b. Please give the answer to two decimal places. 30.03
(b) Find r. Please give the answer to two decimal places. 41.75
(c) Find .
44°
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•
•
•
•
Solve the right triangle.
(a) Find a. Please give the answer to two decimal places. 13.53
(b) Find b. Please give the answer to two decimal places. 41.66
(c) Find B. Give your answer in radians.
Review Problems
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•
•
•
•
Find the exact value for each trigonometric function.
(a) sec 120° –2
(b) tan 390°
(c) cos 315°
Review Problems
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To estimate the height of a mountain above a level plain, the
angle of elevation to the top of the mountain is measured to
be 34 . One thousand feet closer to the mountain along the
plain, it is found that the angle of elevation is 37 .
Estimate the height of the mountain. Please round the
answer to the nearest foot.
6430
Review Problems
25
An airplane is flying at an elevation of 5900 ft, directly above
a straight highway. Two motorists are driving cars on the
highway on opposite sides of the plane, and the angle of
depression to one car is 52 and to the other is 51 .
How far apart are the cars? Please round the answer to the
nearest foot. 9387
Review Problems
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Simplify the following trigonometric expression
tan x
sin 2 x
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Simplify the following trigonometric expression
tan x cos x csc x
1
Simplify the following trigonometric expression
sin(z) + cos(–z) + sin(–z)
cos z
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Simplify the following trigonometric expression
1
Simplify the following trigonometric expression
cos B + sin B tan B
sec B
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29
Simplify the following trigonometric expression
cos 2 x
Simplify the following trigonometric expression
(1 – cos 2 x)(1 + cot 2 x)
1
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Simplify the following trigonometric expression
sin 2 t + cos 2 t + tan 2 t
sec 2 t
Simplify the following trigonometric expression
sec A
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Simplify the following trigonometric expression
2 csc x
Simplify the following trigonometric expression
cot x
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Simplify the following trigonometric expression
sin 2 x
Simplify the following trigonometric expression
tan 2 t
Review Problems
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1.
2.
3.
1
4. -1
-450°
5. 12°
6. 33.51
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
11
28.9
1459 ft
385 ft
t = 447 ft;
w = 163
53,858,204 mi
3300 mi
8.796
31.40177
31.72546
Answers
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
108.9
31.0°
9387 ft
0
30.03
13.53
41.75
44°
41.66
–2
6430
9387
tan x
sin 2 x
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
1
cos z
sec B
1
cos 2 x
1
sec 2 t
sec A
2 csc x
cot x
sin 2 x
tan 2 t
Answers