Question

How do you evaluate $arc\sin \left(\frac{1}{2}\right)$ without a calculator?

Answer 1

Simplify $\arcsin \left(\frac{1}{2}\right)$ without calculator:

The $\arcsin \left(\frac{1}{2}\right)$ give the angle's sine ratio $\frac{1}{2}$.

Then,

$\begin{array}{rcl}\sin \left(\frac{\mathrm{\pi }}{6}\right)& =& \frac{1}{2}\\ & \Rightarrow & arc\sin \left(\frac{1}{2}\right)=\frac{\mathrm{\pi }}{6}\end{array}$

Hence, the value of $arc\sin \left(\frac{1}{2}\right)$ without a calculator is $\frac{\mathrm{\pi }}{6}$.