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

Someone please help! It’s Trigonometry!!!!-example-1
User RPL
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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.


User SHASHANK MADHAV
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