Suppose a Ferris wheel is 100 meters in diameter, and is boarded at ground level. The wheel completes one full revolution every 12 minutes. At time t = 0, an individual is at the 6:00 position (ground level) and ascending.

(a) How many times will the individual be 50 meters off the ground during each complete revolution?

(b) At what times is the individual 50 meters off the ground if the Ferris wheel makes two complete revolutions? (Enter your answers in a comma-separated list.) At $t=$ minutes.

(c) What about four revolutions? (Enter your answers in a comma-separated list.) At $t=$ minutes.

(d) What about five revolutions? (Enter your answers in a comma-separated list.) At $t=$ minutes.

(e) Why is there a pattern to your solutions?

A. Once we find our two base solutions in the first revolution, since it takes 12 minutes for the wheel to complete a full rotation, we keep adding 12 to our two base solutions to get solutions in the subsequent revolutions.

B. There is one base solution and the period of our function is 6, we just keep adding 6 to our base solution to get the rest of the solutions.

C. Every 6 minutes you will get back to the same height on the ferris wheel, so the period of the corresponding function is 6.

D. The period of a trigonometric function is $2\pi$, so all our solutions differ by $2\pi$.

E. There is no pattern.

Hint: