Ferris Wheel Problem

Today in class we did a problem that involves a ferris wheel and how there motion over time is sinusoidal.
EXAMPLE: A ferris wheel with a total height of 55 ft. and a diameter of 50 ft. takes 8 seconds to get to the top from them bottom.

First what you do is sketch a graph like the one to the left with the y-axis being distance from the ground and the x-axis being the time in seconds.

Then from the graph which u have correctly labeled you gather the neccessary information you need to create a sinusoidal equation like the amplitude, sinusoidal axis, period, and phase shift.

In this case the amplitude=25, SA=30, period= 3.14(pi)/8, PS= 0
So with this information you create your equation y=25cos(pi/8*x)+30