Precalculus Homework Help Please

Question

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 90 degrees and the low temperature of 80 degrees occurs at 6 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

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Answer 1

D(t) = Asin(Bt+ C) + D; A = (90 - 80)/2 = 5 degree; D = (80+ 90)/2 = 85 degree. B = 2π/24 = π/2.

So, D(t) = 5sin(πt/12 + C) + 85. Now if t = 6 hours then D(6) = 5sin(π/2 + C) + 85 = 80; sin(π/2 + C) = -1,

π/2 + C = 3π/2; C = π; So, D(t) = 5sin(πt/12 + π) + 85 or D(t) = - 5sin(πt/12) + 85