Trigonometry Ferris Wheel Problem

Question

A Ferris wheel ride varies sinusoidally. When loading, people are 4 feet above the ground. The radius of the Ferris wheel is 60 feet. The ride takes 4 minutes to complete one revolution. if a person starts the ride 10 feet off the ground, give the cosine function of the ride.

f(x)=Acos(Bx-C)+D

I have found:

A=60

Period=4

B=π/2

I cannot find C and D.

Answer 1

D = midline, the average = (2(60)+10+10) = (120+20)/2 = 140/2= 70 = 60+10

max= 130, min=10, D is the midpoint or midline = average of 130 and 10 = 70

C=phase shift

f(x) = AcosB(x-C) +D

=60cos[(pi/2)(x-C)]+70

when x=0, f(x)=10, the starting position

10 =60cos[pi/2)(0-C)]+70

-60=60cos[(pi/2)(-C)]

cos[(-pi/2)(C)] =-1

the cosine of an angle =-1 when the angle =pi

-(pi/2)C = pi

-C/2 = 1

C/2 =-1

C =-2

f(x) =Acos[B(x-C)]+D

f(x) =60cos[(pi/2)(x- -2)] +70

f(x) = 60cos[(pi/2)(x+2)] +70