Sinusoidal temperature ?

Question

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?

? · Answer

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

Sinusoidal temperature ?

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