Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 60 degrees at midnight and the high and low temperature during the day are 80 and 40 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.I don’t understand how my answer is wrong

Answer 1

The range of the sin graph is the difference between the maximum and the minimum temperatures.

range = 80-40

amplituted = range/2 = 20

We also know that the period is 24 hours:

`\begin{gathered} \frac{2\pi}{k\text{ }}\text{ = 24} \\ k\text{ = }(\pi)/(12) \end{gathered}`

When t = 0, temperature = 60

But we are told that the temperature does decrease after midnight so we need to flip the function vertically to make sure that it is still set to decrease and reach a minimum after midnight.

`D(t)\text{ = -20sin\lparen}(\pi)/(12)t)\text{ + 60}`