Daylight function for 40 °N Verify that the function​​ $D(t)=2.8\sin(\frac{2\pi}{365}(t-81))+12$ has the following properties, where t is measured in days and D is the number of hours between sunrise and sunset.

Its maximum and minimum values are 14.8 and 9.2, respectively, which occur approximately at $t=172$  and $t=355$, respectively (corresponding to the solstices).