Question

If $\theta ={\sin }^{-1}[\sin (-600{}^{\circ })],$ then one of the possible values of $\theta$ is:

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\frac{2\pi }{3}$
• D. $-\frac{2\pi }{3}$
• E. 0

Answer 1

Answer: (A)

$\theta ={\sin }^{-1}\{-\sin 600{}^{\circ }\}={\sin }^{-1}\{-\sin 240{}^{\circ }\}$ $={\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)$ $\Rightarrow$ $\theta =60{}^{\circ }=\frac{\pi }{3}$