math
posted by linda .
a ferris wheel has a radius of 8m and rotates every 12 hrs. THe bottom of the ferris wheel is 1m above the ground. draw a graph describing how a person's height above the ground varies with time. Find an qeation for your graph.

sure hope they have a restroom on that ferris wheel if it takes 12 hours to make one rotation.
anyway, I know that the basic shape could be y = 8sin(pi/6)t.
since period = 2pi/k for y = sin kt
and 2pi/k = 12, so k=pi/6
I then shifted this vertically by 9 m to have the person 1 m above the xaxis at the minimum height
But I want him to be only 1 m high when t=0 so I shifted the graph to the right by 3 hours
which gave me y = 8 sin (pi/6)(t  3) + 9
testing:
t=0 y = 1
t=3 y = 9
t=6 y = 17 , maximum height
t=9 y = 9
t= 12 y = 1, it works!!! 
i don't get it. the answer is right but how do you know to shift the graph right by 3 hrs?