Find the principal value of each of the following:\(sin^{-1}(-\frac {\

1.	Find the principal value of each of the following:\(sin^{-1}(-\frac {\sqrt3}2)\)
Answer» Let sin\(^{-1}(-\frac{√3}2)\) = y Then sin y = \((-\frac{√3}2)\) = - sin \((\frac{\pi}3)=\) sin \((-\frac{\pi}3)\) We know that the principal value of sin\(^{-1}\) is \([-\frac{\pi}2,\frac{\pi}2]\) sin\((-\frac{\pi}3)=-\frac{\sqrt3}2\) Therefore the principal value of sin\(^{-1}(-\frac{√3}2)\) is = \(-\frac{\pi}3\)

Find the principal value of each of the following:\(sin^{-1}(-\frac {\sqrt3}2)\)

Answer»

Let sin\(^{-1}(-\frac{√3}2)\) = y

Then sin y = \((-\frac{√3}2)\) = - sin \((\frac{\pi}3)=\) sin \((-\frac{\pi}3)\)

We know that the principal value of sin\(^{-1}\) is \([-\frac{\pi}2,\frac{\pi}2]\)

sin\((-\frac{\pi}3)=-\frac{\sqrt3}2\)

Therefore the principal value of sin\(^{-1}(-\frac{√3}2)\) is = \(-\frac{\pi}3\)