Question

Let θ = sin^–1 (sin (– 600°), then value of θ is ______.

विकल्प

• ${\displaystyle \frac{\pi }{3}}$

• ${\displaystyle \frac{\pi }{2}}$

• ${\displaystyle \frac{2\pi }{3}}$

• ${\displaystyle \frac{-2\pi }{3}}$

Answer 1

Let θ = sin^–1 (sin (– 600°), then value of θ is ${\displaystyle \frac{\pi }{3}}$.

Explanation:

${\displaystyle {\sin }^{-1}\sin (-600\times \frac{\pi }{180})={\sin }^{-1}\sin \left(\frac{-10\pi }{3}\right)}$

= ${\displaystyle {\sin }^{-1}[-\sin (4\pi -\frac{2\pi }{3})]}$

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

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

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

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