Question

Someone please help! It’s Trigonometry!!!!

Answer 1

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


`\sin( (2 \pi t)/20 )`.

Radius of 15 means something like


`15 \sin( (2 \pi t)/20 )`

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


`5 + 15 \sin( (2 \pi t)/20 )`

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


`h(t) = 5 + 15 \cos( (2 \pi t)/20   -  14 \pi / 20)`


`h(t) = 5 + 15 \cos(  (\pi(t  - 7))/(10))`

That may be right.