Question

The average monthly temperature T(m), in degrees Celsius, in a particular city varies according to the model T of m equals 4 times sine of the quantity pi over 6 times m end quantity plus 2 comma where m represents the months since January. Between what months will the temperature be above 0°C?
February and April
January and July
January and April
January and May

Answer 1

Using the given sinusoidal function, it is found that the temperature will be above 0°C between January and July.

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:

$T(m) = 4\sin{\left(\frac{\pi}{6}\right)m} + 2$

Using elementary angles, we have that:

$m = 0, T(m) = 4\sin{0} + 2 = 2$, hence it is positive in January.

$m = 4, T(m) = 4\sin{\left(\frac{2\pi}{3}\right)} + 2 = 5.46$, positive in April.

$m = 6, T(m) = 4\sin{\pi} + 2 = 2$, positive in June.

$m = 7, T(m) = 4\sin{\left(\frac{7\pi}{6}\right)} + 2 = 0$, zero at the end of July.

Hence, it is positive between January and July.

To learn more about sinusoidal functions, you can take a look at https://brainly.com/question/26153754