The height of a piston in a cylinder can be modeled by a sine or cosine function. A piston is at its lowest point in a cylinder, 8cm from the bottom, at t=3.2 seconds.  The piston is at its highest position, 39cm from the bottom, at t=3.6 seconds. Find an equation for the height of the piston, in cm, at any given time t.

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We will use a cosine model. The general model is `y=Acos(B(x-h))+k` where A is the amplitude, B is associated with the period (it is the horizontal compression/stretch), h is the horizontal translation, and k the vertical translation.

(a) The amplitude is

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