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Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5 ft at midnight, rises to a high of 9 ft, falls to a low of 1 ft, and then rises to 5 ft by the next midnight.




What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?


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Answer:

y = 4sin( π/12) + 5

Step-by-step explanation:

For a sinusidal function :

y = Asin(w + c) + s

Where ; A = amplitude ; w= angular velocity, s = vertical Displacement, c = phase angle

A = (maximum - minimum) / 2

A = (9 - 1) /2 = 8/2 = 4 feets

w = 2π/T ; T = 24

w = 2π/24 = π/12

s = (maximum - minimum) / 2

s = (9 +1) /2 = 10/2 = 5

c = 0

Plugging our values into the general equation :

y = Asin(w + c) + s

y = 4sin( π/12) + 5

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