Mississippi daylight

Question

The approximate amount of daylight, D, in hours, in Oxford, Mississippi, can be modeled by the function D(x) = 12 -2cos ((2π/365)(x+10)) where x is the number of days since January 1st. On which day of the year is the amount of daylight at a maximum?

Answer 1

This could be done using calculus (take the derivative and set to 0.0), but note that the maximum daylight hours will occur when the cos function equals -1.

Cos(y) = -1 when y = pi radians, so

2*pi*{x+10) /365 = pi

Solving for x gives ( 2*x +20) / 365 =1

Or

x = 172.5 days

So days 172 and 173 will be the days with the most daylight.