Pre-Calc

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 67 degrees occurs at 5 PM and the average temperature for the day is 60 degrees. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

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  1. the amplitude is 67-60, so start with
    D(t) = 60 + 7 sin(t)
    Since the period is 24 hours,
    D(t) = 60 + 7 sin(π/12 t)
    Since the high occurs at t=17, use cosine, instead of sine.
    D(t) = 60 + 7 cos(π/12 (t-17))

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    oobleck

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