The average monthly temperature changes from month to month. Suppose that, for a given city, we can model the average temperature in a month with the following function.

Question

f(t)= 59 - 26 sin (pi/6 t)

In this equation, f(t) is the average temperature in a month in degrees Fahrenheit, and t is the month of the year (January=1, February=2, ...).

Find the following. If necessary, round to the nearest hundredth.

Number of cycles of f per month :

Answer 1

period T is when (pi/6) t = 2 pi
t = 12 months = period T = 1 year period
f = frequency = 1/T = 1/12 cycle/month (logically enough)

I do not believe it is the mean in Jan and June though. You need a phase angle in there.