Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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1) y = sin  2) y = cos 
3) y = sin  4) y = cos 
A)
B)
C)
D)
a. | 1A, 2D, 3C,
4B | c. | 1B, 2D, 3C,
4A | b. | 1C, 2A, 3B,
4D | d. | 1A, 2B, 3C,
4D |
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2.
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1) y = 2 + sin
x 2) y = 2 + cos x
3) y =
-2 + sin x 4) y = -2 + cos
x
A)
B)
C)
D)
a. | 1A, 2C, 3D,
4B | c. | 1B, 2D, 3C,
4A | b. | 1A, 2B, 3C,
4D | d. | 1A, 2D, 3C,
4B |
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3.
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The function graphed is of
the form    or
 where d is the least possible positive
value. Determine the equation of the graph.
a. | y = cos x -
1 | c. | y = sin x -
1 | b. | y = cos (x +
1) | d. | y = sin (x -
1) |
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4.
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The function graphed is of
the form    or
 where d is the least possible positive
value. Determine the equation of the graph.
a. | y = cos (x -
1) | c. | y = sin x +
1 | b. | y = cos x -
1 | d. | y = sin x -
1 |
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5.
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The function graphed is of
the form    or
 where d is the least possible positive
value. Determine the equation of the graph.
a. | sin x -  | c. | cos  | b. | sin  | d. | sin  |
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6.
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The function graphed is of
the form    or
 where d is the least possible positive
value. Determine the equation of the graph.
a. | cos x -  | c. | sin  | b. | cos  | d. | cos  |
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7.
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Find the amplitude of y =
-2 cos  .
a. | -6 | c. | 3 | b. | 2 | d. |  |
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8.
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Find the amplitude of y =
-4 sin ( 2x + ð).
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9.
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Find the amplitude of y =
-2 sin  .
a. | -8 | c. |  | b. | 2 | d. | 4 |
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10.
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Find the amplitude of y =
-2 cos ( 4x - ð).
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11.
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Find the period of y = -5
sin  .
a. | 8 | c. | 5 | b. |  | d. | ð |
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12.
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Find the period of y = 5
sin  .
a. | 8ð | c. |  | b. | 5ð | d. | 4ð |
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13.
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Find the period of y = 3
cos  .
a. | 3 | c. |  | b. | ð | d. |  |
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14.
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Find the vertical translation
of y = -2 + 2 sin  .
a. | up  | c. | up
6 | b. | down
2 | d. | up  |
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15.
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Find the phase shift of the
function.
y = cos 
a. |  units to the
right | c. |  units
down | b. |  units up | d. |  units to the
left |
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16.
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Find the phase shift of the
function.
y = -2 sin
a. | 4 units
up | c. | 4 units
down | b. |  units to the
right | d. |  units to the
left |
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17.
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Find the phase shift of the
function.
y = -5 cos 
a. |  units to the
left | c. |  units to the
right | b. | 4 units down | d. | 4 units up |
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18.
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Find the phase shift of the
function.
y = -2 sin 
a. | 2ð
units down | c. | 
units to the left | b. | 2ð units up | d. |  units to the
right |
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19.
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Find the phase shift of the
function.
y = -2 sin 
a. | ð units to the
right | c. |  units to the
right | b. |  units to the
left | d. | ð units to the
left |
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20.
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Find the phase shift of the
function.
y = 5 - 3
sin 
a. |  units to the
left | c. |  units to the
right | b. |  units to the
right | d. |  units to the
left |
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21.
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Graph the
function.
y = sin 
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22.
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Graph the
function.
y = cos 
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23.
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Graph the
function.
y = 3 sin 
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24.
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Graph the
function.
y =  cos 
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25.
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Graph the
function.
y = -  sin 
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26.
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Graph the
function.
y = -2 + sin
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27.
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Graph the
function.
y = 1 +
2 cos x
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28.
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Graph the function over a
one-period interval.
y = 3 +  sin (2x -
ð)
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29.
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Graph the function over a
one-period interval.
y =  cos 4 
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30.
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Graph the function over a
one-period interval.
y = 4 + 2 sin(x - ð)
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31.
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Graph the function over a
one-period interval.
y =  cos 2 
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32.
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Graph the function over a
one-period interval.
y =  sin (x + ð)
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33.
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Graph the function over a
one-period interval.
y = 1 + sin(2x-ð)
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34.
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Graph the function over a
one-period interval.
y = -  cos
4(x-ð)
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35.
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A generator produces an
alternating current according to the equation I = 48 sin 109ðt, where t is time in seconds and I is the current in amperes. What is the
smallest time t such that I = 24?
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36.
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A coil of wire rotating in a
magnetic field induces a voltage given by
e = 20 sin  ,
where t is time in seconds. Find the smallest positive time to produce a voltage of
10 .
a. | 2.8ð
sec | c. | 3ð
sec | b. | 3 sec | d. | 2.8
sec |
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37.
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A pendulum of length L, when
displaced horizontally and released, oscillates with harmonic motion according to the equation y = A
sin(( )t + ð/2),
where y is the distance in meters from the rest position t seconds after release, and g = 9.8 m/sec2.
Identify the period, amplitude, and phase shift when A = 0.39 m and  Round all
answers to the nearest hundredth.
a. | 0.31 sec, 0.39 m, -0.079
units to the left | c. | 0.70 sec,
0.39 m, -0.70 units to the left | b. | 1.41 sec, 0.39 m, 0.35 units to the
right | d. | 1.41 sec, 0.39 m, -0.35 units to the
left |
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38.
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Tides go up and down in a
14.8-hour period. The average depth of a certain river is 7 m and ranges from 4 to
10 m. The variation can be approximated by a sine curve. Write an equation that gives the approximate
variation y, if x is the number of hours after midnight and high tide occurs at 5:00
am.
a. | y = 3 sin  | c. | y = 3 sin
 | b. | y = 7 sin  | d. | y = 7 sin  |
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39.
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The temperature in Fairbanks is
approximated by
T(x) = 37 sin  + 25,
where T(x) is
the temperature on day x, with x = 1 corresponding to  and x = 365 corresponding
to Dec. 31. Estimate the temperature on day 49.
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40.
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Ignoring friction, the time , t
(in seconds), required for a block to slide down an inclined plane is given by the formula  where b is the length of the base in feet and  per second is the
acceleration of gravity. How long does it take a block to slide down an inclined plane with a base of
12 feet at an angle of  Round your answer to three decimal
places.
a. | 7.104
sec | c. | 1.252
sec | b. | 0.885 sec | d. | 0.361 sec |
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41.
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Suppose that the average
monthly low temperatures for a small town are shown in the table.
Model
this data using f(x) = a sin(b(x - c)) + d.
a. | f(x) = 23 sin 
+ 42 | c. | f(x) = 23 sin 
+ 42 | b. | f(x) = 42 sin  + 23 | d. | f(x) = 23 sin  +
42 |
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