# Homework Help: Sinusoidal equations

1. Mar 10, 2008

### torrobinson

I have a horrible math teacher this year: she merely shows the steps to solving a problem and doesn't help us understand why and how it works.

1. The problem statement, all variables and given/known data
I need to find the equation for the height of a ferris wheel as it spins. It has a radius of 30m, and a center 18m above ground. It completes a cycle in 60s. The graph starts at the minimum

I think I can write these when the x axis is pi/2, pi, 2pi, etc. But now it's in seconds.

Max = 33m
min=3m

Amplitude is 15
Period is 60s

2. Relevant equations
y=AcosB(X-C)+D

3. The attempt at a solution
A=15
B= (cosine, so 2pi/60 or pi/30 ??????????)
C= (cosine, starting at min, so moved left or right over by 1/2 period so 30???
D= min is 3 meters above ground, so moved upwards period+3 , so 18??

y=15cos((pi/30)(X+30))+18

Now if my domain on my calculator is 0<x<60 and range 0<y<33 , then it looks good vertically, but it starts somewhere above 15 and not 3 ...not moved over enough.

Edit: well that makes no sense. I graphed using an online calculator, and it worked fine. Then I tried on my calculator again and it was off. So I reset my calc. and tried again, and it worked. Is that still the correct answer ^ ?

Last edited: Mar 10, 2008
2. Mar 10, 2008