The general form of the sine function is h(t) = A sin(Bt - C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
In this case, A = 50, B = 2π/10 = π/5, C = 0, and D = 60. The height of the seat varies between 10 and 110 feet.
The period of the sine function is the time it takes for one complete cycle. For the function h(t), one cycle occurs when Bt - C = 2π, or t = (2π + C)/B. Since C = 0 in this case, the period is simply 2π/B.
Therefore, the period of the function h(t) is:
T = 2π/B = 2π/(π/5) = 10
So it takes 10 minutes for the Ferris wheel to make one full revolution