Question

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cosine (StartFraction pi Over 20 EndFraction t). How long does it take for the waterwheel to complete one turn?
5 seconds
10 seconds
20 seconds
40 seconds

Answer 1

Considering the period of the cosine function, it is found that it takes 40 seconds for the wheel to complete one turn.

What is the period of the cosine function?

The cosine function is defined by:

f(x) = acos(bx + c) + d.

For the period, we have to look at coefficient b, and the period is:

P = 2π/|B|

For this problem, the function is given by:

h(x) = 15 cos(π/20)

Hence B = π/20, and the period is:

P = 2π/|B| = 2π/(π/20) = 2 x 20 = 40 seconds.

Hence it takes 40 seconds for the wheel to complete one turn.

More can be learned about the period of trigonometric functions at brainly.com/question/12502943

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