Find the principal value of ${\sin }^{-1}\left(\frac{1}{2}\right)$.

Step-by-step solution

1. The principal value of ${\sin }^{-1}y$ lies in $[-\frac{\pi }{2},\frac{\pi }{2}]$.
2. We need an angle $\theta$ in this interval such that $\sin \theta =\frac{1}{2}$.
3. From the unit circle, $\theta =30^{\circ }=\frac{\pi }{6}$ satisfies the condition and lies in the required interval.
4. Hence the principal value is $\frac{\pi }{6}$.

Concept tested: Principal value of arcsin

Published 2 September 2026 · How this solution was prepared and checked

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