In 2001, Windsor, Ontario received its maximum amount of sunlight, 15.28 hrs, on June 21, and its least amount of sunlight, 9.08 hrs, on December 21.

Question

1) Due to the earth's revolution about the sun, the hours of daylight function is periodic. Determine an equation that can model the hours of daylight function for Windsor, Ontario.

2) On what day(s) can Windsor expect 13.5 hours of sunlight?

Answer 1

the amplitude is (15.28-9.08)/2 = 3.1

Let's say
Jun21 is day 172
Dec21 is day 355
The period is clearly 365 days, so

y = 3.1cos(2π/365 (x-172))

Now just find x when y=13.5 and figure the dates.