Expert answer:Applications of Trigonomic Functions

Answer & Explanation:I have questions about Trigonomic functions.  They are multiple choice.See attached document.Applications of Trigonomic Functions
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Applications of Trig Functions
1.
The length of a day in Philadelphia, Pennsylvania, is given by the sinusoidal function, f(t), which
represents the number of hours of daylight t days into the year:
. How many hours of daylight are there on the twelfth
day of the year? Round the answer to the nearest tenth.
A. 9.1 hours
2.
B. 9.9 hours
C. 12 hours
D. 13.4 hours
The length of a day in Orlando, Florida, is given by the sinusoidal function, f(t), which represents the
number of hours of daylight t days into the year:
.
th
How many hours of daylight are there on the 50 day of the year? Round the answer to the nearest
tenth.
A. 8.2 hours
3.
B. 8.7 hours
C. 9.3 hours
D. 10.3 hours
At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 50
meters and a diameter of 35 meters. It takes the wheel five minutes to make one revolution. Write
the sinusoidal function, f(t), that models the height of your chair at any time, t.
A.
B.
C.
D.
4. At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 100
meters and a diameter of 50 meters. It takes the wheel seven minutes to make one revolution. Write the
sinusoidal function, f(t), that models the height of your chair at any time, t.
A.
B.
C.
D.
5. At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 50
meters and a diameter of 35 meters. It takes the wheel five minutes to make one revolution. If you
start your ride at the midline and the Ferris wheel rotates counter clockwise, how many seconds will
it take for your seat to reach a height of 50 meters? Round the answer to the nearest second.
A. 10 seconds
B. 20 seconds
C. 40 seconds
D. 75 seconds
6. At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 80
meters and a diameter of 40 meters. It takes the wheel seven minutes to make one revolution. If you
start your ride at the midline and the Ferris wheel rotates counter clockwise, how many seconds will
it take for your seat to reach a height of 60 meters? Round the answer to the nearest second.
A. 0 seconds
B. 10 seconds
C. 20 seconds
D. 40 seconds
7. The temperature in your house is controlled by a thermostat. The temperatures will vary according to
the sinusoidal function:
, where f(x) represents the temperature
in degrees Celsius (°C) and x is hours since midnight. What is the temperature of your house at 9:00 a.m.?
A. 5°C
B. 16°C
C. 19°C
D. 25°C
8. The temperature in your house is controlled by a thermostat. The temperatures will vary according
to the sinusoidal function:
, where f(x) represents the
temperature in degrees Celsius (°C) and x is hours since midnight. What is the minimum temperature
of your house?
A. 13°C
B. 16°C
C. 19°C
D. 24°C
9. The temperature in your house is controlled by a thermostat. The temperatures will vary according
to the sinusoidal function:
, where f(x) represents the
temperature in degrees Celsius (°C) and x is hours since midnight. What is the minimum temperature
of your house?
A. 5°C
B. 16°C
C. 19°C
D. 24°C
10. The population of rabbits varies with respect to time, in days, as a sinusoidal function. The graph
below represents the variation in population. From the graph determine the amplitude.
A. 10
B. 15
C. 17
D. 28
11. (Using the same graph as No. 10) The population of rabbits varies with respect to time, in days, as a
sinusoidal function. The graph below represents the variation in population. From the graph
determine the horizontal shift.
A. 10
B. 15
C. 17
D. 28
12. A group of scientists found a new species of spider in the desert. The body temperature of the spider
appears to vary sinusoidal over time. A maximum body temperature of the spider reaches 125° after 15
minutes from the start of the examination. Then, 14 minutes later, the body temperature falls to a
minimum of 99°. The scientists would like to write an equation to model the body temperature of the
spider over time. Which function will model their findings?
A.
B.
C.
D.
13. The function
is used to represent the changes in temperature of a
chemical compound used in a lab. What is the amplitude?
A. 22
B. 6
C.
D. 80
14. The function
is used to represent the changes in temperature of a
chemical compound used in a lab. What is the phase shift?
A. 22
B. 6
C.
D. 80
15. The function
is used to represent the changes in temperature of a
chemical compound used in a lab where t is measured in minutes since the beginning of the experiment.
What is the temperature after five minutes? Round the answer to the nearest degree.
A. 95°
B. 90°
C. 85°
D. 80°
…
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