Question

A ferris wheel has a radius of 20m and the bottom is 2m above the ground. The wheel makes one rev in 40 sec. If the rider gets on at 30^0 on the left of the lowest point going downwards, wirte the sine function to show this movement

Answer 1

the axle is at height 2+20 and the amplitude is 20, so we can start with

f(t) = 22+20sin(t)

we want a period of 40 seconds, so 2π/k=40, making k=π/20

f(t) = 22+20sin(π/20 t)

-cos(x) achieves its minimum at x=0, so since we want our minimum at 30°, which is 1/12 of a period, or at t=10/3

f(t) = 22-20cos(π/20 (t-10/3))

Now, cos(x) = sin(π/2-x), so you can massage that into the sine curve

f(t) = 22-20sin(π/20 (t+20/3))

the wolframalpha page confirms that this has a minimum at t=10/3, or 1/12 of a period. That is, 30° after starting.

http://www.wolframalpha.com/input/?i=22-20sin(%CF%80%2F20+(20%2F3%2Bt))