Answer
The given statement makes sense.
Work Step by Step
The statement talks about the periodicity of the sine function, so the period of the sine function is $2\pi $, or it can be written as
$\sin \left( x+2\pi \right)=\sin x$
So,
$\begin{align}
& \sin \frac{7\pi }{3}=\sin \left( 2\pi +\frac{\pi }{3} \right) \\
& =\sin \frac{\pi }{3} \\
& =\frac{\sqrt{3}}{2}
\end{align}$
So, by using the periodic properties of the sine function, the exact value of $\sin \frac{7\pi }{3}$ can be calculated.
Hence, the statement is true.
