Mathematics, 05.11.2020 19:10 leeshaaa17
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 97 degrees during the day and the average daily temperature first occurs at 10 AM. How many hours after midnight, to two decimal places, does the temperature first reach 82 degrees?
Answers: 2
![y=A\sin[\omega(x-\alpha)]+C](/tpl/images/0870/7961/fd847.png)
, α= phase shift on the Y-axis and C = midline.
[midline is average of upper and lower limit.]
![y=12\sin[\dfrac{\pi}{12}(x-10)]+85](/tpl/images/0870/7961/3f1fe.png)
![82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03](/tpl/images/0870/7961/6049b.png)
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