A) \[\frac{4\pi }{3}\]
B) \[\frac{5\pi }{3}\]
C) \[-\frac{2\pi }{3}\]
D) \[-\frac{\pi }{3}\]
Correct Answer: D
Solution :
Key Idea: The principal value of \[{{\sin }^{-1}}x\]is\[-\frac{\pi }{2}\]to \[\frac{\pi }{2}.\] We have \[{{\sin }^{-1}}\left( -\frac{\sqrt{3}}{2} \right)=\theta \] \[\Rightarrow \] \[\sin \theta =-\frac{\sqrt{3}}{2}\] \[=-\sin \frac{\pi }{3}\] \[=\sin \left( -\frac{\pi }{3} \right)\] \[\therefore \] Principal value is \[\left( -\frac{\pi }{3} \right).\]
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