Sinusoidal temperature ?

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 58 and 92 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after midnight, to two decimal places, does the temperature first reach 63 degrees?

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  • Bryce
    Lv 7
    3 weeks ago

    y= asin[b(x - c)] + d

    a= (92 - 58)/2= 17

    b= 2π/24= π/12

    (π/12)(8 - c)= 0; c= 8

    d= (58 + 92)/2= 75

    T(t)= 17sin[(π/12)(t - 8)] + 75  

    63= 17sin[(π/12)(t - 8)] + 75

    sin[(π/12)(t - 8)]= -12/17

    (π/12)(t - 8)= arcsin(-12/17)

    t - 8= 12arcsin(-12/17)/π

    t≈ 5.01 hours

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