Find the value of sin 31 3 - Vidyadip

Question

Find the value of sin $\begin{equation} \frac{31 \pi}{3} \end{equation}$

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Answer

Let y = sin $\begin{equation} \frac{31 \pi}{3} \end{equation}$
We know that values of sin x repeat after an interval of 2$\pi$. Therefore
$\begin{equation} \sin \frac{31 \pi}{3}=\sin \left(10 \pi+\frac{\pi}{3}\right)=\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2} \end{equation}$

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