Explain solution in detail: Length of time from sunrise to sunset (in hours) t days after the Spring Equinox is given by l(t)=12+4sin(pi t/182)

a) Sketch l(t)

(b) What is the length of the shortest and the longest day and when do these occur accord-

ing to this formula?

(c) Find the average day-length over the month immediately following the equinox.

(d) Find the average day length over the whole year. Explain your result with a simple

geometric or intuitive argument. Answer:b)about 13 hours, c)12 hours for 364 days.