Answer
$365$ days
Yes, it is expected.
Work Step by Step
Using the sine function $y=a\sin b(x-c)+d$, rewrite the given function:
$$C=21.6\sin \frac{2\pi }{365}\left(t+\frac{3978.5}{2\pi}\right)+30.3$$
From the function, $b=\frac{2\pi}{365}$.
Finding the period:
$$period=\frac{2\pi}{b}=\frac{2\pi}{\frac{2\pi}{365}}=365$$
Thus, the period is $365$ days.
Yes, it is expected as there are $365$ days in one year.
