Find the principal value of each of the following :

Question:

Find the principal value of each of the following :

$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)$

Solution:

$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=\sin ^{-1}\left(\sin \left(\pi-\frac{\pi}{3}\right)\right)$

[ Formula: $\sin (\pi-x)=\sin x$ )

$=\sin ^{-1}\left(\sin \frac{\pi}{3}\right)$

[ Formula: $\sin ^{-1}(\sin x)=x$ ]

$=\frac{\pi}{3}$

 

Leave a comment

None
Free Study Material