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Question

Mathematics Question on Trigonometric Functions

The principal value of sin⁡−1(−32)\sin^{-1} \left( - \frac{\sqrt{3}}{2} \right) is :

A

−π3 - \frac{\pi}{3}

B

π6 \frac{\pi}{6}

C

−2π3 - \frac{2 \pi}{3}

D

2π3\frac{2\pi}{3}

Answer

−π3 - \frac{\pi}{3}

Explanation

Solution

sin⁡−1(−32)=[sin⁡−1sin⁡(−π3)]=−π3\sin^{-1} \left( - \frac{\sqrt{3}}{2}\right) = \left[\sin^{-1} \sin\left( - \frac{\pi}{3}\right)\right] = - \frac{\pi}{3}