Notice that the coldest time of day is when sin((2π(t+1))/24)=1. Solving for t we get:
[tex]\begin{gathered} \sin (\frac{2\pi(t+1)}{24})=1 \\ \frac{2\pi(t+1)}{24}=\frac{\pi}{2} \\ 2(t+1)=12 \\ t+1=6 \\ t=5 \end{gathered}[/tex]
Therefore the coldest time of a day is 5 hours after midnight
