Question

Evaluate ${\sin }^{-1}(\sin 2)$

Answer 1

To evaluate : ${\sin }^{-1}(\sin 2)$

${\sin }^{-1}\left(\mathrm{sin\theta }\right)$ $=\theta$ if $\frac{-\mathrm{\pi }}{2}\le \mathrm{\theta }\le \frac{\mathrm{\pi }}{2}$

⇒ ${\sin }^{-1}\left(\sin 2\right)={\sin }^{-1}\sin (\mathrm{\pi }-2)$

$=(\mathrm{\pi }-2)$

Thus,${\sin }^{-1}\left(\sin 2\right)$$=(\mathrm{\pi }-2)$