Pre-Calculus: Ch 6.1 through 6.6 PRACTICE Set
Name: _______________________________
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the
question.
____ 1. Graph the function. Which choice gives the amplitude, period, phase shift,
and vertical shift for the function?
y
a.
–2
2
O
y
c.
10
10
–2
–10
2
3
4;
;–
–10
1
9
;1
O
;–
2
y
10
–2
O
–10
4;
2
3
Short Answer
;–
1
9
; –1
1
9
d.
10
–2
2
3
4;
y
b.
2
O
–10
;1
4;
2
3
;–
1
9
;1
2
Pre-Calculus: Ch 6.1 through 6.6 PRACTICE Set
Name: _______________________________
2. Write an equation of the sine function with the given amplitude, period,
phase shift, and vertical shift.
amplitude: 4, period = 23 , phase shift = – 12 , vertical shift = –2
3. The normal monthly temperatures (F) for Omaha, Nebraska, are recorded
below.
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1
2
3
4
5
6
7
8
9 10 11 12
t
Temp. 21 27 39 52 62 72 77 74 65 53 39 25
a. Write a sinusoidal function that models Omaha’s monthly temperature
variation.
b. Use the model to estimate the normal temperature during the month of
April.
4. A merry-go-round ride has outer horse figures which go up and down
exactly three times during one rotation of the carousel. One of the
high-points for each horse occurs where a rider is just close enough to
reach out and try to grab a metal ring from a mechanical dispenser. If the
rider succeeds in grabbing a brass ring instead of an iron ring, the rider has
won a free ride on the merry-go-round. Hence the expression, “reaching for
the brass ring.” Write a sinusoidal function that models the height of one of
the horse figures as a function of the rotation of the main carousel with  =
0 at the ring dispenser. The amplitude of the horse’s vertical motion is 1.1
meters around an average height of 1.6 meters.
5. The mean average temperature for Fairbanks, Alaska, is 27° F. The
monthly average temperatures vary between 36.5° above and below this
value. If t = 0 represents February, the phase shift of the sine function is 2.
a. Write a model for the average monthly temperature in Fairbanks, Alaska.
b. According to your model, what is the average temperature in November?
Pre-Calculus: Ch 6.1 through 6.6 PRACTICE Set
Name: _______________________________
6. Barnacles on a wharf are 2.5 feet out of the water at low tide and 7.3 feet
below water at high tide. Write a sine function that models the water level
relative to the barnacles, if the period from high tide to high tide is 12.5
hours and the phase shift for high tide is 2.85 hours.
7. Jan observes a buoy bobbing up and down through a total (crest to trough)
amplitude of 8 feet. Beginning at the top of the wave, if the buoy completes
a full cycle every 8 seconds, what is the height of the buoy relative to its
lowest point after 12 seconds?
8. A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. At
t = 0, a certain point is at height 0. What is the height of the point above the
ground after 15 seconds?
9. Stan observes a raft floating on the water bobbing up and down through a
total amplitude of 5 feet. Beginning at the top of the wave, if the raft
completes a full cycle every 5 seconds, what is the height of the raft
relative to its lowest point after 32 seconds?
10. Change 4.74 radians to degree measure. Round to the nearest tenth.
11. Change
to radian measure in terms of .
12. For a circle of radius 4 feet, find the arc length s subtended by a central
angle of
13. Find the area of a sector with a central angle of
millimeters. Round to the nearest tenth.
and a radius of 8.6
14. Jack’s bicycle tires have a diameter of 24 inches. If he rides at 10 miles per
hour, what is the angular velocity of the wheels in revolutions per minute
(rpm)?
15. A gear of radius 4.6 cm turns at 3 revolutions per second. What is the linear
velocity of the gear in centimeters per second?
Pre-Calculus: Ch 6.1 through 6.6 PRACTICE Set
Name: _______________________________
16. State the amplitude, period, phase shift, and vertical shift for the function.
Then graph the function.
17. Write an equation of the sine function with the given amplitude, period,
phase shift, and vertical shift.
amplitude: 3, period = 4 , phase shift = 12 , vertical shift = –4
18. The sun always illuminates half of the moon’s surface, except during a
lunar eclipse. The illuminated portion of the moon visible from Earth varies
as it revolves around Earth resulting in the phases of the moon. The period
from a full moon to a new moon and back to a full moon is called a synodic
month and is 29 days, 12 hours, and 44.05 minutes long. Write a sine
function that models the fraction of the moon’s surface which is seen to be
illuminated during a synodic month as a function of the number of days, d,
after a full moon. [Note: full moon equals illuminated.]