Question

Tony visits the local fair and sees one of the rides, the ferris wheel. The ferris wheel has a diameter of 50 feet and is on a platform of 4 feet. If it takes 12 seconds to make one full revolution, what is the equation of the height of a person on the ferris wheel at any time t?

Answer 1

assuming the person starts at the wheel's lowest position when t=0, that means that f(t) will look something like

f(t) = -cos(t)

The radius is 25 feet, so that makes it

f(t) = -25cos(t)

The axle is 25+4=29 feet off the ground, so

f(t) = 29-25cos(t)

since cos(kt) has period 2π/k, we have 2π/k = 12, so

f(t) = 29-25cos(π/6 t)

Answer 2

We could use either a sine or a cosine function, you did not specify which, but I will use sine

It must be of the type
height = a sin k(Ø + d) + c
period = 12 s
= 2π/k
2π/k = 12
k = 2π/12 = π/6

also we know a = 25

so far we have
height = 25 sin π/6(t + d) + c

you did not say where you want the person to be when t = 0 , that will determine the phase shift

you did not say how the height you want relates to the 4 foot platform. Do you want your height to describe the height above ground or above the platform.