Can you help please? Look at description for problem. There were too many characters to fit in the title portion. Thank you!

Question

A Ferris wheel has a diameter of 220 feet and the center of the wheel is 125 feet above the ground. The wheel makes a complete turn every 2 minutes. Write a cosine function to express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes), given that the passenger is at the lowest point on the wheel when t=0.

Answer 1

The cos functions is in this form: f(x) = A cos B(x + C) + D

A is the amplitude

2π/B is the period

C is the horizontal shift

D is the vertical shift

We can take each piece of what is given and plug it into the equation.

Since the diameter = 220, the amplitude will be half of that, 110=A

The Ferris wheel has a period of 2 minutes, the time it takes to make one full revolution.

2π/B=2

B=π

The center is 125 ft off the ground, the is the vertical shift.

D=125

The are telling you that the Ferris wheel is at the lowest point when t=0. Normally the parent function shows cos at the highest point. This can be accomplished one of 2 ways.

Option 1 is add a negative sign and have it reflect on the x axis.

f(x) = -110 cos (πx) + 125

Option 2 is you can also add a phase shift of half the period to the left. Half the period is 1.

f(x) = 110 cos π(x + 1) + 125