# 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?

### 1 Answer

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- BryceLv 73 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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