Most times we don't really need angles to do trig, believe it or not. But circular motion is really the case where we do.
A period of 20 seconds is a frequency of 1/20 is something like

.
Radius of 15 means something like

The top being 35 meters while the diameter is 30 meters must mean it's mounted five feet off the ground.

Seven seconds to reach the top must mean we're 7/20 th of the circle away from the top. We'll switch to cosine so a zero argument is the maximum. We introduce a phase offset so that t=7 hits the maximum


That may be right.