# The monthly average temperature T (in °C) in a certain city, may be approximated by T(t) = a cos[ b(t – d) ] + c

The monthly average temperature T (in °C) in a certain city, may be approximated by

T(t) = a cos[ b(t – d) ] + c

where t is the time in months, t = 0 corresponds to January 1 st, and we assume that function T(t) has a period of 12 months.

a) Find a, b (b > 0), c and d if T has a maximum of 22.4 °C in the middle of July (t = 6.5) and a minimum of – 10 °C.

b) In which month is T minimum?

c) Over how many months is T greater than 18 °C?