(A) We know that the value of $\sin x$ repeats after an interval of $2 \pi$. Therefore,we can write: $\sin \frac{31 \pi}{3} = \sin \left( 10 \pi + \fr

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(A) We know that the value of $\sin x$ repeats after an interval of $2 \pi$. Therefore,we can write: $\sin \frac{31 \pi}{3} = \sin \left( 10 \pi + \frac{\pi}{3} \right)$ Since $\sin(2n \pi + \theta) = \sin \theta$ for any integer $n$,we have: $\sin \left( 10 \pi + \frac{\pi}{3} \right) = \sin \frac{\pi}{3}$ Finally,the value is: $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$

Class 11 Mathematics Trigonometric Functions Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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Find the value of $\sin \frac{31 \pi}{3}$.

A
$\frac{\sqrt{3}}{2}$
B
$-\frac{\sqrt{3}}{2}$
C
$\frac{1}{2}$
D
$-\frac{1}{2}$

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Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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Find the value of $\sin \frac{31 \pi}{3}$.

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