A carnival ferris wheel that has a diameter of 18m, goes 4 seconds every revolution, there are 5 revolutions, also the ferris wheel is 2m above the ground

Question

Cosine and Sine equation needed

Answer 1

you don't say at what point the wheel starts. Let's say that at t=0 the point of interest at the bottom of the rotation.

Since cos(t) starts at the top, we know right away that the function will look like

y = -cos(kt)

The diameter is 18, so the radius is 9, and we now have

y = -9cos(t)

But, the starting chair is 2m above the ground, rather than 9m below, so

y = -9cos(t) + 11

The period is for seconds, so

y = -9cos(π/2 t) + 11

No sure what to do with the 5 rotations thing. That means the ride lasts 20 seconds. What a rip-off!

As for the sine function, you know that cos(x) = sin(π/2 - x) so fit that in.

Or, consider that an unshifted sine function would start when the loading chair was at axle height.