Question

Unit testIn January, the average temperature t hours after midnight in Mumbai, India, is given byT(t) = 24.5 – 5.5 sin(21(t+1)24What is the coldest time of day in Mumbai? Give an exact answer.

Answer 1

Notice that the coldest time of day is when sin((2π(t+1))/24)=1. Solving for t we get:

`\begin{gathered} \sin ((2\pi(t+1))/(24))=1 \\ (2\pi(t+1))/(24)=(\pi)/(2) \\ 2(t+1)=12 \\ t+1=6 \\ t=5 \end{gathered}`

Therefore the coldest time of a day is 5 hours after midnight