Exam 3 Review-Chpts. 4,5&6 MTH 140
Precalculus
Name_____________________
1)
Fill in the values in the table below from
memory. (On the exam you be
asked to do this without the aid of your notes or calculator.)
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0° |
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30° |
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45° |
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60° |
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90° |
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180° |
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2)
Find
the exact value of: (On
the exam you be asked to do this without the aid of your notes or calculator.)
a)
b) 
c) 
d) 
e)
f) 
g) 
h) 
i) 
j) 
k) 
l) 
3) Each of the following is an angle in
standard position. Determine the
quadrant in which the angle lies.
a) 160º b) -291º
4) Find the angle of smallest possible
positive measure coterminal with the given angle.
a) -230º b) 575º
5) Find the length of the arc of a circle
of radius 20.02 cm subtended by a central angle of 0.6 radians.
6) Convert the degree measure to
radians. Express your answer as a
multiple of 
.
a) 162º b) -480º
7) Convert -157º to radians, correct to
two decimal places. Use 3.1416 for .
8) Convert the radian measure to
degrees. Round to the nearest hundredth
only when necessary.
a) 
b) 
c) 4 d) -1.02
9) A wheel of radius 1.5 feet is moving
forward at 18 feet per second. How fast
is the wheel rotating?
10) Given that 
11) Use an identity to find the value of each
expression.
a) 
b) 
12) Two sides of a right triangle ABC
(C is the right angle) are given.
Find the indicated trigonometric function of the given angle. Give exact answers.
a) 
b) 
13) A hiker climbs for a half mile up a slope
whose inclination is 17°. How many feet of altitude, to the nearest
foot, does the hiker gain?
14) Given that 
is a point on the
terminal side of angle 
, find 
.
15) Name the quadrant in which the angle lies.
a) 
b) 
16) a) 
b) 
17) Graph the following functions.
a) 
b) 
c) 
d) 
18) An experiment in a wind tunnel generates
cyclic waves. The following data is
collected for 44 seconds.
|
Time (in
seconds) |
Wind
Speed (in
feet per second) |
|
0 |
14 |
|
11 |
34 |
|
22 |
54 |
|
33 |
34 |
|
44 |
14 |
Let
V represent the wind speed (velocity) in feet per second and let t
represent the time in seconds. Write a
sine equation that describes the wave.
19) Graph the function 
20) Find the value of the given expressions.
a) 
b) 
c) 
d) 
e) 
21) Write 
as an expression in x.
22) Solve the right triangle.
a) 
b) 
23) A surveyor is measuring the distance
across a small lake. He has set up his
transit on one side of the lake 140 feet from a piling that is directly across
from a pier on the other side of the lake.
From his transit, the angle between the piling and the pier is 70º. What is the distance between the piling and
the pier to the nearest foot?
24) A straight trail with a uniform
inclination of 14º leads from a lodge at an elevation of 900 feet to a mountain
lake at an elevation of 9800 feet. What
is the length of the trail to the nearest foot?
25) The distance that an object travels in t
seconds is given by 
. Find:
a) the
maximum displacement from its resting position
b) the
time required for one oscillation
c) the
frequency
26) Verify the identity:
a) 
b) 
c) 
d) 
e) 
f) 
g) 
h) 
27) Find the exact value using a sum or
difference identity.
a) 
b) 
c) 
28) Given that 
29) 
30) Use an identity to write 
as a single
trigonometric function.
31) Solve the following equations on the
interval 
.
a) 
b) 
c) 
d) 
e) 
f) 
g) 
32) Find the missing parts of the triangle.
a) 
b) 
c) 
d) 
33) A surveyor standing 69 meters from the
base of a building measures the angle to the top of the building and finds it
to be 35º. The surveyor then measures
the angle to the top of the radio tower on the building and finds that it is
48º. How tall is the radio tower?
34) Two points A and B are on
opposite sides of a building. A surveyor
selects a third point C to place a transit. Point C is 45 feet from point A
and 67 feet from point B. The
angle ACB is 50º. How far apart
are points A and B?
Key
