function D(x) = 12 -2cos ((2π/365)(x+10))

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?

the answer given does not provide details

Answer 1

set the angle = pi, so the cosine =-1

then D=14 hours of daylight= max

2pi/365(x+10)= pi

2x+20=365

x=345/2=172.5

173rd day of the year

= about the summer solstice or june 22

which is what you'd get even without the model, for the northern hemisphere