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Find the value of \(sin^{-1}⁡(sin⁡ \frac{4π}{3})\) is _______(a) π(b) \(\frac{π}{3}\)(c) \(\frac{4π}{3}\)(d) –\(\frac{π}{3}\)I got this question in final exam.Question is from Inverse Trigonometric Functions Basics topic in chapter Inverse Trigonometric Functions of Mathematics – Class 12

Answer»

Correct OPTION is (d) –\(\frac{π}{3}\)

To elaborate: \(SIN^{-1}⁡(sin⁡X)\)=x, x∈\([-\frac{π}{2},\frac{π}{2}]\)

∴\(sin^{-1} (sin⁡ \frac{4π}{3})=sin^{-1}⁡(sin⁡(π+\frac{π}{3}))=sin^{-1}⁡(sin⁡(\frac{-π}{3}))= -\frac{π}{3}\).


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