Math Help - Shifting functions

1. Shifting functions

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, 8 cm from the bottom at t = 3.2 seconds. The piston is at its highest at 39 cm, at t=3.6 seconds

I'm trying to find an equation for this function but I can't seem to get it right

So far I got 15.5 cos ( (something)x - 3.6) +23.5

I've switched things around and I'm forgetting how to shift the function's period, I know the cosine function has a period of pi, but I want it to be 0.4, since its high and low are between 3.6 and 3.2 seconds

2. Originally Posted by realintegerz
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, 8 cm from the bottom at t = 3.2 seconds. The piston is at its highest at 39 cm, at t=3.6 seconds

I'm trying to find an equation for this function but I can't seem to get it right

So far I got 15.5 cos ( (something)x - 3.6) +23.5

I've switched things around and I'm forgetting how to shift the function's period, I know the cosine function has a period of pi, but I want it to be 0.4, since its high and low are between 3.6 and 3.2 seconds
With all the given data one possible function which models the movement of the piston is:

$f(x)=-15.5 \cdot \cos \left(\dfrac{5\pi}2 (x-3.2)\right) + 23.5$

I've attached the graph of this function and I've marked the time-interval in question.