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Transforming Trig Unit Assignment
DROPBOX: Transforming Trig Unit Assignment
The following questions are to be answered with full solutions. Be sure to focus on proper
mathematical form, including: (6)
One equal sign per line
Equal signs in each question lined up vertically with each other
No self-developed short form notation
One step or idea per line (do not do steps in your head that are not written down; each
line must represent a step-by-step progression from question to answer)
1. The average monthly temperatures in New Orleans, Louisiana, are
given in the following tables: (14)
Month J F M A M J
°C 16.5 18.3 21.8 25.6 29.2 31.9
Month J A S O N D
°C 32.6 32.4 30.3 26.4 21.3 18.0
a. What is the range of this function?
b. What is the average yearly temperature?
c. Is this function sinusoidal? Fully explain your answer.
d. Graph the data using a scatter plot. Does this confirm the
answer from question 1c?
e. Given the general sinusoidal function T(t) = asin[b(t – c)] + d,
what do a, b, c, and d represent?
f. What characteristics of the function correspond to the constants a, b, c, and d?
g. Determine the temperature function T(t). [Hint: Consider January to be Month 0,
February to be Month 1, etc.]
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2. In 2001, Windsor, Ontario received its maximum amount of sunlight,
15.28 hrs, on June 21, and its least amount of sunlight, 9.08 hrs, on
December 21. (10)
a. Due to the earth’s revolution about the sun, the hours of daylight function is periodic.
Determine an equation that can model the hours of daylight function for Windsor,
b. On what day(s) can Windsor expect 13.5 hours of sunlight?
3. Tides are cyclical phenomena caused by the gravitational pull of the sun and the moon.
On a particular retaining wall, the ocean generally reaches the 3 m mark at high tide. At
low tide, the water reaches the 1 m mark. Assume that high tide occurs at 12:00 p.m.
and at 12:00 a.m., and that low tide occurs at 6:00 p.m. and 6:00 a.m. What is the
height of the water at 10:30 a.m.? (10)
4. The largest Ferris Wheel in the world is the London Eye in England. The height (in
meters) of a rider on the London Eye after t minutes can be described by the function
h(t) = 65 sin[12(t − 7.5)] + 70. (15)
a. What is the diameter of this Ferris wheel?
b. Where is the rider at t = 0? Explain the significance of this value.
c. How high off the ground is the rider at the top of the wheel?
d. At what time(s) will the rider be at a height of 100 m?
e. How long does it take for the Ferris wheel to go through one rotation?
f. What is the minimum value of this function? Explain the significance of this value.
5. At Canada’s Wonderland, a thrill seeker can ride the Xtreme
Skyflyer. This is essentially a large pendulum of which the rider is the bob. The height
of the rider is given for various times: (20)
Time(s) 0 1 2 3 4 5 6 7 8 9
Height(m) 55 53 46 36 25 14 7 5 8 15
a. Create a graph of the height of the pendulum with respect to time.
b. Find the amplitude, period, vertical translation, and phase shift for this function.
[Note: the table does not follow the bob through one complete cycle, so some
thought will be required to answer this question.]
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c. Determine the equation of the function in the form:
h(t) = asin[b(t – d)] + c.
d. How could the amplitude be determined without creating the graph or finding the
e. What would the rest position of the pendulum be?
f. What is the maximum displacement for this pendulum?
g. The time for one complete cycle is the period. How long
would it take to complete 15 cycles?
6. A mass suspended on a spring will exhibit sinusoidal motion when it moves. If the mass
on a spring is 85 cm off the ground at its highest position and 41 cm off the ground at
its lowest position and takes 3.0 s to go from the top to the bottom and back again,
determine an equation to model the data. (10)
Assessment OF: This assignment will be evaluated for a grade or mark that will contribute to your overall final mark in this course.