Trigonometry

Suppose you were at the beach and notice that at 1:00 pm the tide is in, that is, the depth of water is at its deepest. At that time you find that the depth of the water at the end of the pier is 1.9 meters. At 7:00 that evening when the tide is out, the depth of the water is 1.1 meters. Assuming that the depth of the water varies sinusoidally with time, find an equation that will model the depth of the water.

A. y=1.5cos(pi/3(x-7)) + 0.4

B. y=1.5cos(pi/6(x-7)) + 0.4

C. y=0.4cos(pi/6(x-7)) + 1.5

D. y=-0.4cos(pi/6(x-7)) + 1.5

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asked by John
  1. half-period is 6 hours, so a full period is 12 hours. So, if 2pi/k = 12, k = pi/6.

    The max-min=1.9-1.1 = 0.8, so the amplitude is 0.4

    So, the choice is C or D.

    The midpoint is (1.9+1.1)/2 = 1.5, so we're still looking at C or D.

    Since we apparently want a cosine function, whose minimum is at x=7, that would make it (D) since (C) has its max at x=7.

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    posted by Steve

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