Write a sinusoidal equation

Question

A Ferris wheel is 36 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position of the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 9 minutes. What is the height of the rider after 2 minutes into the ride?

Answer 1

If the wheel starts 1 meter above ground and it is 36 meters in diameter then the midpoint will be at one half of 36 + 1=19 which is your vertical shift

Amplitude is 18

Period is 2pi/b. So b=2pi/9 Radians

There is no phase shift

Since you start at the bottom this is best modeled as a negative cosine graph

y= -18cos(2pi t/9) +19

At t= 2 minutes y = -18cos(4pi/9) +19

y= -18cos(1.3962) +19

y= -3.126 +19= 15.87 meters