Question

Create both a sine and cosine model for height of a passenger off of the ground for each of the following Ferris wheels.

1) customers must climb up 12 foot steps to get into the Ferris wheel (I.e) bottom of Ferris wheel is at the top of the steps
Diameter 67ft
Rotional speed 1 revolution every 80 seconds

2) customers gets into a Ferris wheel 17 feet below ground level (bottom of Ferris wheel is at that level)
Diameter 122ft
Rotional speed 1 revolution 150 seconds

My issue is that I don't know how to deal with the below and walking up steps and how to account for that when creating the functions. I just need the parameters for example
Amplitude =A
Vertical shift =K
Phase shift =h
Period =b
h(t)=acos(b(t-h))+k
h(t)=asin(b(t-h))+k

Answer 1

well, where is the center of the wheel above ground?
12 + 67/2 = 45.5 = center above ground
It does not say where the wheel starts so I will say it is at height = bottom
now in general
h = 45.5 + 33.5 sin( 2 pi t/T -p)
where T is period in seconds and p is phase in radians
Now I want it at the bottom or 12 ft when t = 0
that means sin (argument) = -1
or ( 2 pi t/T - p) = -pi/2
when t = 0
so
p = pi/2
so
h = 45.5 + 33.5 sin( 2 pi t/T - pi/2)

for the cos function, same deal but
h = 45.5 + 33.5 cos( 2 pi t/T -p)
now I want cos arg = -1 at t = 0
cos = -1 when p = pi or -pi radians
so
h = 45.5 + 33.5 cos( 2 pi t/T -pi)