Trig ferris wheel problem help?

Question

Here are some facts about a given ferris wheel:

 - The diameter of the wheel is approximately 472 feet

 - Assume the bottom of the wheel is 9 feet off the ground

 - It takes 36 minutes for this wheel to make one complete rotation

Let y=the height of one of the cars and x = time in minutes. If at time x=0, the cabin is at the middle of the wheel, write an equation in the form y=a sin(b(x-c))+d to model the height of the cabin.

Answer 1

If you setup the coordinate system such the origin is 9 ft below the bottom of the ferris wheel & the y axis going through the center of the ferris wheel circle, you can find x & y as

(Let a = theta , the angle of the ferris wheel turning counterclockwise).

y = 245 + 236sin(a) and x = 236cos(a) but a = wt where w = angular velocity = 2*pi/36= pi/18

and a = pi*t/18 and t = time in minutes

I could not put my information into the exact type equation you have above (probably because of my choice of coordinate system) but y in terms of x in my coordinate system is y = 245 +- 236sin{cos^-1(x/236)}

In terms of time, y = 245 + 236sin(pi*t/18) where t=0 coincides with the cabin at point (236, 245)