Question

The number of hours of sunlight in a day of a leap year, in part of Ontario, can be
modelled by a sinusoidal function with a minimum of 8.9 on the 356th day of the year
(December 21st), and a maximum of 15.4 on the 173rd day of the year (June 21st).
a. Find a sinusoidal function that models this relationship. [5 marks]
b. What days (on the calendar) are the closest to 14 hours in length? [4 marks]
c. How long is the 218th day of a leap year? [1 mark]

Answer 1

Final answer:
The sinusoidal function that models the number of hours of sunlight in Ontario over a leap year is H(t) = 3.25 cos[2m / 365 × (t -
356)] + 12.15. The days when the length of daylight is closest to 14 hours, and the length of the 218th day, can be obtained by solving this equation for the respective values of t.