Question

A Ferris wheel has a diameter of 380 feet and the center of the wheel is 195 feet above the ground. The wheel makes a complete turn every 4 minutes. Write a cosine function to express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes), given that the passenger is at the lowest point on the wheel when t

Answer 1

y = -190 cos(π t / 120) + 195

Explanation:

General form of a sinusoidal function: y = A cos(Bt - C) + D

Now generally a cosine function starts at the maximum value, so to start at the minimum value, flip the cosine function by making it negative.

A is the amplitude of the curve and will be the radius of the ferris wheel. Therefore, A = 380 / 2 = 190 feet.

2π / B is the period of the curve and will be the time to complete one full rotation. The time to complete one full rotation is given as 4 minutes. Convert this into seconds to get period = 4 minutes * (60 seconds / minute) = 240 seconds. Therefore, B = 2π / period = 2π / 240 seconds = π / 120.

C/B is the phase shift, or horizontal shift of the graph. Since the negative cosine function already starts at the minimum value, there is no phase shift so C/B = 0, meaning C = 0.

D is the vertical shift and will be the height of the center of the ferris wheel. Therefore, D = 195 feet.

Your final function will be:

y = -190 cos(π t / 120) + 195