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Q.
The principal value of $\sin^{-1} \left(\sin \frac{2\pi}{3}\right) $ is:
Inverse Trigonometric Functions
Solution:
Let $\sin^{-1} \left( \sin \frac{2 \pi}{3} \right) = \theta$
$\Rightarrow \, \sin \theta = \sin \frac{2 \pi}{3}$
Note: Principle value of sin x lies between
$ \frac{- \pi}{2} $ and $\frac{\pi}{2}$
So, here $\sin\theta = \sin\left(\pi- \frac{\pi}{3}\right) = \sin \frac{\pi}{3}$
Therefore, principle value of
$ \sin^{-1} \left(\sin \frac{2 \pi}{3}\right) $ is $\frac{\pi}{3} $