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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
Question
Find the principal value of $\sin ^ { - 1 } \left( - \frac { 1 } { 2 } \right).$
✓

Answer

Let $y = \sin^{-1}\left(-\frac{1}{2}\right)$
$\sin y = \frac{-1}{2}$
$\sin y = \sin \left(\frac{-\pi}{6}\right)$
Range of principal value of $\sin^{-1}$ is between $\frac{-\pi}{2}$ and $\frac{\pi}{2}$
Hence, the principal value is $\frac{-\pi}{6}$

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