# math (sinusoidal functions

The height of the rider on a Ferris Wheel can be modeled by a cosine function. At time t = 0, a rider
boards the Ferris Wheel at its minimum height of 3 m. The maximum height of the Ferris Wheel is 39
m. During the 8 minute ride, the rider reaches the minimum height 5 times (including the times at t = 0
and t = 8 minutes).
a) Sketch the height of the Ferris wheel versus time for the first 8 minutes. Include a proper scale, axis
labels, the axis of the curve and the maximum and minimum heights.
[3]
b) Determine an equation to model the height of the rider after t minutes.
[4]
c) How many times during the first 8 minutes will the rider be at a height of 10 m? Justify your answer

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1. see the graph at

http://www.wolframalpha.com/input/?i=plot+y%3D21-18cos(pi+t),y%3D3,y%3D39+for+0%3C%3Dt%3C%3D8

use what you know about periods, amplitudes and shifting to see how it works.

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