Question

I don’t understand this can someone help it’s a practice test please show steps.

Answer 1

Using the sinusoidal function, it is found that the temperature will be below 0ºC between May and August.

What is a Sinusoidal function?

• A sinusoidal function is a function that depends on a trigonometric function, having peaks according to the period and amplitude given by this function.

The function for the average monthly temperature, in m months after January, is given by:

$T(m) = 10\cos{\left(\frac{\pi}{6}\right)m} + 5$

Working with elementary angles, we have that:

$m = 10, T(0) = 10\cos{0} + 5 = 15$

$m = 3, T(3) = 10\cos{\left(\frac{\pi}{2}\right)} + 5 = 5$

$m = 6, T(3) = 10\cos{\pi} + 5 = -5$

$m = 9, T(3) = 10\cos{\left(\frac{3\pi}{2}\right)} + 5 = 5$

$m = 12, T(3) = 10\cos{2\pi} + 5 = 5$

From this, we have that it becomes negative after March, and positive before September, removing the middle two options.

Now, we have to test for April and May, that is, m = 4 and m = 5, hence:

$m = 4, T(4) = 10\cos{\left(\frac{2\pi}{3}\right)} + 5 = 0$

$m = 5, T(5) = 10\cos{\left(\frac{5\pi}{6}\right)} + 5 = -3.66$

Negative only in May, hence the temperature will be below 0ºC between May and August.

To learn more about sinusoidal function, you can take a look at brainly.com/question/18055768