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Trigonometry Problem

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In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled approximately by a trigonometric function.

The lowest temperature is usually around 3C, and the highest temperature is around 18C. The temperature is typically halfway between the daily high and daily low at both 10 a.m., and 10 p.m. and the highest temperatures are in the afternoon.

Find the formula of the trigonometric function that models the temperature T in Johannesburg t hours after midnight. Define the function using radians.

I got the points mixed up again... T-T

Is it: (10, 3C), (3C, 10),  (-10, 18C), or, (18C, -10). Or are all of those options wrong, and is it some other option?

Thank you!~

Jul 28, 2020

#1
+25532
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In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled approximately by a trigonometric function.

The lowest temperature is usually around 3C, and the highest temperature is around 18C.

The temperature is typically halfway between the daily high and daily low at both 10 a.m., and 10 p.m.

and the highest temperatures are in the afternoon.

Find the formula of the trigonometric function that models the temperature T in Johannesburg t hours after midnight.

$$\begin{array}{|rcll|} \hline \dfrac{18^\circ C + 3^\circ C}{2} &=& 10.5^\circ \\ \\ \dfrac{18^\circ C - 3^\circ C}{2} &=& 7.5^\circ \\ \\ \hline \mathbf{T} &=& \mathbf{10.5^\circ C+7.5^\circ C\cdot\sin\Bigg(\left(\frac{t+2}{12}-1\ \right)\cdot\pi \Bigg)} \\ \hline \end{array}$$

Jul 28, 2020
#2
+55
+1

Thank you so much!~

TheLovely1  Jul 28, 2020