Answer:
Minimum average temperature is 33 °F
Number of cycles of f per month is

Time for one full cycle is 12 months
Explanation:

where:
- f(t) = the average temperature a month in °F
- t = month of the year
As
, the range of the sine part of the function is:
Therefore the minimum temperature will be when


The period of the sine curve is the length of one cycle of the curve. The period is the distance between the peak and the next peak (or trough and the next trough).
To find this algebraically, set the sine part of the function to 26 and solve for t:




Therefore the period of this function is 12 months.
So the number of cycles of f per month is

and the time for one full cycle of f is 12 months.