At a certain latitude in the northern hemisphere, the

At a certain latitude in the northern hemisphere, the numbers d of hours of daylight in each day of the years is taken to be d = A + B . sin kt , where A, B, k are positive constants and t is the time in days after spring equinox. a. Assuming that the number of hours of daylight follows an annual cycle of 365 days, find the value of k, giving your answer correct to 3 decimal places. b. Given also that the shortest and longest days have 6 and 18 hours of daylight respectively, state the value of A and B. Find, in hours and minutes, the amount of daylight on new years day, which is 80 days before the spring equinox.