Question

What is ${\sin }^{-1}\sin \frac{3\pi }{5}$ equal to ?

• A. $\frac{3\pi }{5}$
• B. $\frac{2\pi }{5}$
• C. $\frac{\pi }{5}$
• D. None of the above

Answer 1

The correct option is B $\frac{2\pi }{5}$

To find ,

${\sin }^{-1}\sin \left(\frac{3\pi }{5}\right)$

Consider graph of ${\sin }^{-1}\sin x$

We know that,

$\frac{\pi }{2}<\frac{3\pi }{5}<\pi$

And, for $\theta ϵ(\frac{\pi }{2},\frac{3\pi }{2})$

${\sin }^{-1}\sin \theta =\pi -\theta$

$\Rightarrow {\sin }^{-1}\sin \left(\frac{3\pi }{5}\right)$$=\pi -\frac{3\pi }{5}$

$=\frac{2\pi }{5}$

Hence, B is correct.