Xavier is riding on a Ferris wheel at the local fair. His height can be modeled by the equation H(t) = 20 cospi over 15t + 30, where H represents the height of the person above the ground in feet at t seconds.

Part 1: How far above the ground is Xavier before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?

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Question

Xavier is riding on a Ferris wheel at the local fair. His height can be modeled by the equation H(t) = 20 cospi over 15t + 30, where H represents the height of the person above the ground in feet at t seconds.

Part 1: How far above the ground is Xavier before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?

You must show all work.