Question

assume the camera is placed 6 feet from the center of the merry-go-round and the diameter of the merry-go-round is 6 feet. build a trigonometric function that models the distance (feet) of the rider from the camera as a function of time (seconds). be sure to use function notation to express your function model.

Answer 1

The trigonometric function that models the distance (feet) of the rider from the camera as a function of time (seconds) is γ(t) = ωt, where ω is the angular velocity of merry-go-round.

Let, center of the merry-go-round is C and camera is placed at point A. B(t) define the position of the rider at any time t. The angle between these three-point A, C and B is y(t). Radius (r) of the merry-go-round is 3 feet and distance (d) of the rider from the camera is 6 and the angular velocity of the rider is ω.

Assume the rider is at the edge of the merry-go-round (as the position is not specified). So, the length of CB(t) is r. To solve this problem lets consider that angular velocity of merry-go-round is constant,  ω = 0 and y(t) = 0.

Therefore, we have y(t) = ωt

So, the the distance (feet) of the rider from the camera is (from the triangle AB(t)C)

C(t) = √(r² + d² - 2rdcos(y(t)) = √(45 - 36cos(ωt) = 3√(5 - 4cos(ωt))

Learn more about angular velocity here:

brainly.com/question/14769426

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