Question

The principal value of sin${}^{-1}\left(sin\frac{2\pi }{3}\right)$ is

• A. $-\frac{2\pi }{3}$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{3}$
• D. $\frac{5\pi }{3}$

Answer 1

Answer: (C)

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