Answer:
define the height above the ground, h, as a function of time, t, using the sine function:
h(t) = A * sin(B * t + C) + D
A represents the amplitude of the function, which is half of the vertical distance covered by the rider (in this case, 30 feet).
B represents the frequency of the function, which is related to the number of complete cycles or revolutions in a given time period. In this case, the Ferris wheel completes 2 revolutions per minute, so B = 2π (since 2π radians represents one complete revolution).
C represents the phase shift of the function, which accounts for the initial position of the rider. Since the rider starts at the lowest point, there is no phase shift, so C = 0.
D represents the vertical displacement of the function, which is the average height above the ground. In this case, the center of the wheel is 30 feet above the ground, so D = 30.
Putting it all together, the trigonometric function that can be used to model the rider's height, h(t), above the ground after t seconds is:
h(t) = 30 * sin(2π * t) + 30
Therefore, the sine function can be used to model the rider's height