Precalculus math help

Question

A ferris wheel is 50 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.

amplitude=25meters

midline=27meters

period=4minutes

How high are you off the ground after 2 minutes?

Answer 1

if it takes 4mins to complete a full revolution that means in 2mins you have completed a half revolution so starting at the 6o'clock position you are now at the 12o'clock position so the highest point: you start 2m off the ground then go up the full 50m of diameter so you are 50+2=52m off the ground

the math if you would like is you start at the lowest point so the function is -cos, amplitude 25, period 4 so 2pi/4=pi/2, vertical shift is 27m so equation

-25cos(x*pi/2)+27, plug in 2 for x: -25cos(2*pi/2)+27=-25cos(pi)+27=25+27=52m