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The outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the

temperature is 68°F at midnight and the high and low temperatures during the day are 80°F and 56°F, respectively.

Assuming t is the number of hours since midnight, nd a function for the temperature, D, in terms of t.

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  1. 30 May, 11:11
    0
    D = - 12sin (π/12) (t) + 68

    Step-by-step explanation:

    Let temperature D in terms of number of hours t be given as:

    D = asinkt + 68

    Now,

    The difference between high and low temperatures is = 80-56 = 24 °F

    The period is = 24 hours

    So, we have 2π/k = 24

    Or, k = 24/2π

    Now,

    Let a = 12 hours

    So, our equation becomes

    D = 12sin (2π/24) (t) + 68

    This is valid for 12 hours gap. If we want to implement for whole day then

    D = - 12sin (π/12) (t) + 68

    Put t=0

    D = 68°F which is temperature at midnight

    Put t=6

    D = - 12 (1) + 68

    D = 56°F

    Put t=18

    D = - 12 (-1) + 68

    D = 80°F
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