Urgent Trig Ferris Wheel Question

Question

A Ferris wheel has a max height of 100 feet, and a minimum height of 8 feet (radius of 46 feet). The Ferris wheel makes 1 rotation every 3 minutes, and the initial angle is 3pi/4. What is the equation in the form of f(x) = Asin(Bx - C) + D

Answer 1

sines and cosines model cyclical behavior, like a ferris wheel

but they both have amplitude from -1 to +1 or a difference between max and min of 2

This ferris wheel has max 100 and min 8, with a difference of 92. It's height will vary between -46 and +46 above and below its mean height of 108/2 = 54.

So you need to shift the standard sine or cosine curve or equation up from 0 to 54, then elongate its amplitude so instead of +1, you get 100 and instead of -1 you get 8. Instead of zero, you get 54

sin0 = 0 you want Asin(Bx-C) + D = 54

Make D=54, and A = 46

when at a maximum height of 100, 46sin(pi/2) + 54 = 100

That gives you A and D

Now all you need is B and C

Bx+C = 3pi/4 = initial angle when x = 0 or at time zero

so B(0) + C = 3pi/4

C = 3pi/4

we're down to f(x) = 46sin(Bx+ 3pi/4) + 52

Just find B and also worry about multiple solutions that repeat every 2pi

One piece of unused information is that it rotates once every 3 minutes. You want

Bx to indicate a full cycle that repeats when x goes from 0 to 3, and 3 to 6, etc.

In the standard sine curve, sinx repeats as x goes from 0 to 2pi

You want sinBx to repeat as x goes from 0 to 3

sinB(0) = 0 and sinB(3) = 0

3B is the angle whose sine = 0

3B=0 + 2npi where n = any integer

3B = 2npi

B = 2npi/3

Answer 2

All I can tell you is that the diameter is 92'.

The circumference is d*pi=289.026.........'

Speed=289/3=96.34ft/min; or 1.6ft/sec.

As for rpm: .666......