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Question: The principal value of \(\sin ^ { - 1 } \left( \sin \frac { 5 \pi } { 3 } \right)\) is...

The principal value of sin⁡−1(sin⁡5π3)\sin ^ { - 1 } \left( \sin \frac { 5 \pi } { 3 } \right) is

A

5π3\frac { 5 \pi } { 3 }

B

−5π3- \frac { 5 \pi } { 3 }

C

−π3- \frac { \pi } { 3 }

D

4π3\frac { 4 \pi } { 3 }

Answer

−π3- \frac { \pi } { 3 }

Explanation

Solution

sin⁡−1(sin⁡5π3)=sin⁡−1(−32)=−π3\sin ^ { - 1 } \left( \sin \frac { 5 \pi } { 3 } \right) = \sin ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 2 } \right) = - \frac { \pi } { 3 }