Problems and solutions for Review #1 - Missouri State University

Group/In-Class Exercises Name___________________________________
8/18/09 g0401Larson8eTrig.tst
4.1 Radian and Degree Measure
MULTIPLE CHOICE. Choose the one alternative that best
completes the statement or answers the question.
The given angle is in standard position. Determine the
quadrant in which the angle lies.
1) -157°
A) Quadrant II B) Quadrant I
C) Quadrant IV D) Quadrant III
Find the radian measure of the central angle of a circle of
radius r that intercepts an arc of length s.
2) r = 1 meter, s = 700 centimeters
A) 700 radians B) 70 radians
C) 1
radians D) 7 radians
700
Convert the angle in degrees to radians. Express answer as
a multiple of π.
3) - 160°
A) - 7
9π
π radians B) -
9 10 radians
C) - 7π
8
radians D) - 8π
9 radians
Convert the angle in radians to degrees. Round to two
decimal places.
4) 4π
7 radians
A) 102.86° B) 104.86°
C) 103.86° D) 101.86°
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Draw the angle in standard position.
5) 330°
6) - 7π
6
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1
MULTIPLE CHOICE. Choose the one alternative that best
completes the statement or answers the question.
Find a positive angle less than 360° that is coterminal with
the given angle.
7) - 4π
9
A) 23π
9
C) 32π
9
B) 4π
9
D) 14π
9
Solve the problem.
8) A car wheel has a 14-inch radius. Through
what angle (to the nearest tenth of a degree)
does the wheel turn when the car rolls forward
1 ft?
A) 54.1° B) 59.1°
C) 49.1° D) 64.1°
9) A carousel has a radius of 20 feet and takes 35
seconds to make one complete revolution.
What is the linear speed of the carousel at its
outside edge? Express the answer in feet per
second. If necessary, round the answer to two
decimal places.
A) 3.59 feet per second
B) 11 feet per second
C) 125.66 feet per second
D) 0.57 feet per second

Answer Key
Testname: G0401LARSON8ETRIG
1) D
2) D
3) D
4) A
5)
6)
7) D
8) C
9) A
2

Solutions: Group/In-Class Exercises
4.1 Angles and Radian Measure - Trig: PBCC
For text: Precalculus Larson 8e
E:\My Documents All\My Documents USB\Math\xGroup\group_trig_f10_PC_Larson8\g0401Larson8eTrig_sol.doc
4.1

Group/In-Class Exercises Name___________________________________
8/18/09 g0401Larson8eTrig.tst
4.2 Trigonometric Functions: The Unit Circle
MULTIPLE CHOICE. Choose the one alternative that best
completes the statement or answers the question.
The point P on the unit circle that corresponds to a real
number t is given. Find the values of the indicated
trigonometric function at t.
1) 5 2 6
, -
7 7
A) 7
5
C) -
7 6
12
Find csc t.
B) 5
7
D) - 6
10
Use the unit circle to find the value of the trigonometric
function.
2) sin 3π
2
A) 0 B) -1
C) 1 D) undefined
Find the exact value of the expression if θ = 45°. Do not
use a calculator.
sin θ
3)
6
A)
C)
2
12
6 2
2
B)
2
6
D) 12 2
Solve the problem.
4) The force acting on a pendulum to bring it to
its perpendicular resting point is called the
restoring force. The restoring force F, in
Newtons, acting on a string pendulum is given
by the formula
F = mg sinθ
where m is the mass in kilograms of the
pendulum's bob, g ≈ 9.8 meters per second per
second is the acceleration due to gravity, and θ
is angle at which the pendulum is displaced
from the perpendicular. What is the value of
the restoring force when m = 0.5 kilogram and
θ = 45°? If necessary, round the answer to the
nearest tenth of a Newton.
A) 3.4 N B) 3.3 N
C) 4.2 N D) 3.5 N
1
Use even and odd properties of the trigonometric
functions to find the exact value of the expression.
5) sec - π
6
A) -2 B) -
C)
2 3
3
D) 2
2 3
3
Use an identity to find the value of the expression. Do not
use a calculator.
6) csc2 π
4
- cot2 π
4
A) -1 B) π
4
C) 1 D) - π
4
Use periodic properties of the trigonometric functions to
find the exact value of the expression.
7) tan 35π
6
A) - 3 B)
C) - 3
3
3
3
D) 3
Use a calculator to find the value of the trigonometric
function to four decimal places.
8) cot 0.2775
A) 1.0398 B) 0.9617
C) 3.5106 D) 0.2848
Solve the problem.
9) The height of the water, H, in feet, at a boat
dock t hours after 7 A.M is given by
E = 5 + 4 cos π
t, where t is time measured in
25
seconds. Find the period.
A) π
50
B) 1
50
C) 50 D) 50π

Answer Key
Testname: G0402LARSON8ETRIG
1) C
2) B
3) A
4) D
5) C
6) C
7) C
8) C
9) C
2

Solutions: Group/In-Class Exercises
4.2 Trig Functions: Unit Circle - Trig: PBCC
For text: Precalculus Larson 8e
E:\My Documents All\My Documents USB\Math\xGroup\group_trig_f10_PC_Larson8\g0402Larson8eTrig_sol.doc
4.2

Group/In-Class Exercises Name___________________________________________________
8/30/10 0403Larson8eTrig.tst
4.3 Right Angle Trig
MULTIPLE CHOICE. Choose the one alternative that best
completes the statement or answers the question.
Two sides of a right triangle ABC (C is the right angle) are
given. Find the indicated trigonometric function of the
given angle. Give an exact answer with a rational
denominator.
1)
Solve.
2
Find sin �.
A) sin � =
C) sin � =
5
29
2
5 29
29
B) sin � =
D) sin � =
29
5
2 29
29
2) Given that sin � = 3
and that the terminal side
5
is in quadrant II, find tan �.
A) 4
3
C) 3
4
B) - 3
4
D) - 4
3
3) Given that sin � = 3
and that the terminal side
5
is in quadrant II, find cot �.
A) - 4
3
C) - 3
4
B) 5
3
D) 5
4
Solve the problem.
4) A radio transmission tower is 250 feet tall.
How long should a guy wire be if it is to be
attached 10 feet from the top and is to make an
angle of 22° with the ground? Give your
answer to the nearest tenth of a foot.
A) 667.4 feet B) 269.6 feet
C) 258.8 feet D) 640.7 feet
dbad
1

Group/In-Class Exercises 8/30/10 0403Larson8eTrig.doc - Solutions
4.3 Right Angle Trig

Group/In-Class Exercises Name___________________________________________________
8/30/10 0404Larson8eTrig.tst
4.4 Trig Functions of Any Value Larson8e
MULTIPLE CHOICE. Choose the one alternative that best
completes the statement or answers the question.
A point on the terminal side of angle � is given. Find the
exact value of the indicated trigonometric function of �.
1) (4, 9) Find tan �.
A) 9
10
C) 9
4
B) 4
9
D) 2
5
Let � be an angle in standard position. Name the quadrant
in which the angle � lies.
2) sec � < 0, tan � < 0
A) quadrant IV B) quadrant I
C) quadrant II D) quadrant III
Find the exact value of the indicated trigonometric
function of �.
3) tan � = 20
, 180°< � < 270° Find cos �.
21
A) -21 B)
C)
-21 41
41
20 41
41
D) - 21
29
Find the reference angle for the given angle.
4) -426°
A) 24° B) 66°
C) 114° D) 156°
5) 9�
8
A) 9�
8
C) �
8
B) 7�
8
D) �
16
Use reference angles to find the exact value of the
expression. Do not use a calculator.
6) csc -2�
3
A) - 1
2
C) -
2 3
3
B) - 3
D) - 2
1
7) cot -17�
6
A) -
3
3
C) 3 D)
ccdbccc
B) - 3
3
3

Group/In-Class Exercises 8/30/10 0404Larson8eTrig.tst - Solutions
4.4 Trig Functions of Any Value