Question

A ferris wheel is 35 meters in diameter and boarded at ground level. The wheel makes one full rotation every 8 minutes, and at time t = 0 you are at the 9 o'clock position and descending. Let f(t) denote your height (in meters) above ground at t minutes. Find a formula for f(t).

Answer 1

F(t) = -17.5sin((t/4)*pi) + 17.5
Because the ferris wheel is a circle you can use sine and cosine. As we are descending and in the middle of the descent the use of negative sine makes the most sense.
Period = 2pi.
Our period is 8 minutes.
8 minutes*w = 2pi
w = (t/4) * pi.
The 17.5 at the end is to take into account that we are 17.5 meteres up in the air at the start.

Answer 2

I personally think it is f(t) = 17.5 sin (π/4)(-t+6) + 17.5