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Using Monotonicity to Find the Range of a Function

Find the valu...

Question

Find the value of the expression :
${sin}^{- 1} (sin \frac{2 π}{3}) .$

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Solution

Given :
${sin}^{- 1} (sin \frac{2 π}{3})$
We know that the range of the principal value branch of ${sin}^{- 1} x$ is $[- \frac{π}{2}, \frac{π}{2}]$ .
$∴ {sin}^{- 1} (sin (π - \frac{π}{3}))$
$= {sin}^{- 1} (sin (\frac{π}{3})) = \frac{π}{3}$
Hence, the value of the expression is $\frac{π}{3} .$

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Using Monotonicity to Find the Range of a Function

Standard XII Mathematics

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