# A system of solar panels produces a daily average power P that changes during the year. It is maximum on the 21 st of June (day with the highest number of daylight) and equal to 20 kwh/day.

A system of solar panels produces a daily average power P that changes during the year. It is maximum on the 21 st of June (day with the highest number of daylight) and equal to 20 kwh/day. We assume that P varies with the time t according to the sinusoidal function
P(t) = a cos [b(t – d)] + c
where t = 0 corresponds to the first of January, P is the power in kwh/day and P(t) has a period of 365 days (28 days in February). The minimum value of P is 4 kwh/day.
a) Find the parameters a, b, c and d.
b) Sketch P(t) over one period from t = 0 to t = 365.
c) When is the power produced by the solar system minimum?.
d) The power produced by this solar system is sufficient to power a group of machines if the power produced by the system is greater than than or equal to 16 kwh/day. For how many days, in a year, is the power produced by the system sufficient?