Question

principal value of sin^-1(sin2pi/3)​

Answer 1

Answer:

$\sin {}^{ - 1} ( \sin( \frac{2\pi}{3} ) ) \\= \sin {}^{ - 1} ( \sin(\pi - \frac{2\pi}{3} ) ) \\= \sin {}^{ - 1} ( \sin( \frac{\pi}{3} ) )\\ = \frac{\pi}{3} \\ since \: \: \frac{\pi}{3} \in[ { - \frac{\pi}{2} },{ \frac{\pi}{2} } ]$