Take the following expression into account:
[tex]D(t)=3\sin (\frac{\pi}{6}t)+12[/tex]Since the term:
[tex]3\sin (\frac{\pi}{6}t)[/tex]Is between -3 and 3 depending on the specific value of t, we know that:
[tex]\begin{gathered} -3<3\sin (\frac{\pi}{6}t)<3 \\ \Rightarrow-3+12<3\sin (\frac{\pi}{6}t)+12<3+12 \\ \Rightarrow9<3\sin (\frac{\pi}{6}t)+12<15 \\ \Rightarrow9Therefore, the hours of daylight range from at least 9 hours and at most 15 hours.