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A Ferris wheel with a diameter of 60 completes 2 revolutions in one minute. The center of the wheel is 30 feet above the ground. If a person taking a ride starts at the lowest point, which trigonometric function can be used to model the riders height, h(t), above the ground after t seconds?

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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

User Thanasis M
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