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Question: The principal value of \(\sin ^ { - 1 } \left( \frac { - \sqrt { 3 } } { 2 } \right)\) is...

The principal value of sin⁡−1(−32)\sin ^ { - 1 } \left( \frac { - \sqrt { 3 } } { 2 } \right) is

A

−2π3- \frac { 2 \pi } { 3 }

B

−π3- \frac { \pi } { 3 }

C

4π3\frac { 4 \pi } { 3 }

D

5π8\frac { 5 \pi } { 8 }

Answer

−π3- \frac { \pi } { 3 }

Explanation

Solution

sin⁡−1[sin⁡(−π3)]=−π3\sin ^ { - 1 } \left[ \sin \left( - \frac { \pi } { 3 } \right) \right] = - \frac { \pi } { 3 } (∵−π2<sin⁡−1x<π2)\left( \because - \frac { \pi } { 2 } < \sin ^ { - 1 } x < \frac { \pi } { 2 } \right)