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
[tex]\sin( (2 \pi t)/20 )[/tex].
Radius of 15 means something like
[tex]15 \sin( (2 \pi t)/20 )[/tex]
The top being 35 meters while the diameter is 30 meters must mean it's mounted five feet off the ground.
[tex]5 + 15 \sin( (2 \pi t)/20 )[/tex]
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
[tex]h(t) = 5 + 15 \cos( (2 \pi t)/20 - 14 \pi / 20)[/tex]
[tex]h(t) = 5 + 15 \cos( \dfrac{\pi(t - 7)}{10})[/tex]
That may be right.
