Mathematical Investigations III
Name
Mathematical Investigations III
Trigonometry - Modeling the Seas
INTERESTING APPLICATIONS
Problem 1: Ferris Wheel
You climb into a chair on a Ferris wheel. The chair, which is at its lowest point, is 2 ft from the
ground, and the wheel has a diameter of 40 ft. The wheel moves a bit, stops to pick up more
passengers and moves a bit more. When all of the seats are filled, you are several feet above the
ground. The Ferris wheel begins to revolve at a continuous rate of one revolution every two
minutes. You observe your watch and it takes 7 seconds for you to reach the top. Your height
measured in feet above the ground, after t seconds is a sinusoidal curve.
a.
What is the period?
b.
Draw the graph of your height as a
function of time.
h
What is the min height?
What is the max height?
What is the amplitude?
What is the phase shift if you use a
cosine function as a model for this
behavior?
t
c.
Write the equation of the cosine function that represents your height after t seconds.
d.
How many feet above the ground were you when the Ferris wheel started moving
continuously?
e.
At what time did you first reach a height of 8 feet?
f.
When was the second time you reached a height of 8 feet?
Trig. 17.1
Rev. S05
Mathematical Investigations III
Name
Problem 2: Tides
The depth of the water is measured at the end of a boat dock that extends into the ocean. On one
particular day, low tide is at 2:15 PM and the depth of the water is found to be 1.5 meters. High
tide was at 8:27 PM when the depth was found to be 4.3 meters. Let t represent the number of
hours after noon. The depth d of the water follows a sinusoidal curve.
a.
Find the period in hours.
b.
Sketch the graph of the depth of the
tide.
td
Find the amplitude.
Find the phase shift if you use a cosine
function as a model for this behavior.
c.
Write the equation of the cosine function that gives the depth of the water in terms of the
time past noon.
d.
How deep was the water at noon?
e.
How deep will the water be at 10 PM?
f.
At what time will the water first be 4 meters deep?
g.
When is the third time after noon that the water will be 2 meters deep?
Trig. 17.2
Rev. S05