How would i go about creating and solving this sinusoidal function

Question

As you ride the London Eye (a Ferris wheel), your distance from the ground varies sinusoidally with time. You are the last seat filled and the wheel starts immediately. You find that it takes you 15min to reach the top (135m above the ground), and the wheel makes a revolution once every 30min. The diameter of the wheel is 120 metres.

1. Write an equation to represent the height of the rider on the London Eye above the ground as a function of time. Include a sketch of the function with your work.
2. What is the height of the rider nearest metre at 6 minute

Answer 1

If the peak height is 135 and the diameter is 120 that means that the loading platform is at 15m. The midline will therefore be at (125 +15)/2 =75 which is you d value

Amplitide or A vale is the radius which is 60

period is 2pi/b so 30 =2pi/b and b = pi/15

Finally since you are starting at the bottom this is a -cosine graph with no phase shift

So equation is y = -60cos(pi/15)x +75

to find the height at 6 minutes substitute 6 for x

y= -60cos(6pi/15) +75

y= -60(.309) +75= 56.45m