Question

After how many days will there be 12 hours of sunlight for the first time during the year?

Answer 1

In order to have 12 hours of sunlight, the value of the sine will need to be zero, this way S(t) = 12.

The sine can be zero when the argument is 0 or the argument is pi:

`\begin{gathered} \sin(0)=0 \\ \sin(\pi)=0 \end{gathered}`

Since sin(0) is the first day of the year (t = 0), let's use sin(pi):

`\begin{gathered} S(t)=12+2\sin((2\pi)/(365)t)\\ \\ S(t)=12\\ \\ 2\sin((2\pi)/(365)t)=0\\ \\ (2\pi)/(365)t=\pi\\ \\ (2)/(365)t=1\\ \\ t=(365)/(2) \end{gathered}`

Therefore the correct option is the second one.