Question

How do you find the exact values of ${\sin }^{-1}\left(\frac{1}{2}\right)$ ?

Answer 1

Compute the required value.

Let ${\sin }^{-1}\left(\frac{1}{2}\right)=x$

So, $\frac{1}{2}=\sin x$

Since, in the principal value range $\left[-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right]$ or $\left[-90°,90°\right]$ the value of $\sin \theta$ is $\frac{1}{2}$ for $\theta =30°$.

Thus, $\frac{1}{2}=\sin \left(30°\right)$

Therefore, $x=30°$

Hence, the exact value of ${\sin }^{-1}\left(\frac{1}{2}\right)$ is $30°$.