Trigonometry question

Question

A Ferris wheel at the Circus has a diameter of 100 feet. The wheel completes a full rotation in 40 minutes at a speed which allows passengers to enter a capsule at the base of the Ferris wheel without stopping the wheel. At the highest point a capsule reaches a height of 115 above the ground. The height above the ground,of a capsule in x minutes after it starts at the base of the Ferris wheel can be modeled by

f(x) = Acos(pi/20 times x) + B. What are the values of A and B?

Consider a capsule that begins its rotation at the base of this Ferris wheel. At which times shown will the capsule be 90 meters above the ground? Select all that apply.

all numbers are in minutes 5 7 15 30 33 65

Answer 1

A gives you the amplitude: the distance from the midline to either extreme in height. Since the diameter of the ferris wheel is 100 feet, the passenger goes from 50 feet above the midline to 50 feet below the midline. The amplitude is 50.

B gives you the vertical shift: how high is the midline above the ground? The highest point is 115 feet. The midline is 50 meters below that (the amplitude). So the midline is at 65 feet. The vertical shift is 65 feet.

When will the capsule be 90 meters above the ground? 90 meters is about 295 feet. So never.