Equation of the circle

Question

A Ferris wheel has a radius of 31.3 feet. The center of the Ferris wheel is 37.4 feet above the platform from which riders board, as demonstrated in the following sketch. Assuming that the x-axis lies along the top of the platform, and the y-axis passes through the center of the Ferris wheel, find an equa tion of the circle that represents the Ferris wheel.

Answer 1

a sinusoidal equation

y = Asin(B(x-C)+ D

D= midline, height of the center

A = amplitude

2pi/B = period

C=phase shift

if it's center is 37.4 with a radius of 31.3 then it's lowest point is 6.1 feet off the ground level. lowest point in the equation will be when sin(B(x-C) = -1 and B(x-C) = 270 degrees or 3pi/2 radians

midline = D = 37.4

A = 31.3

y= 31.3sin(B(x-C)) + 37.4

information from the sketch probably includes the time and provides enough to calculate B and C, plug those values in for the full equation. but no sketch appears.

You could also use a cosine fuction if so, C, the phase shift will be different.