$Iff\left(x\right)=\left|\sin x\right|hasaninverseifitsdomainis$

$\begin{array}{l}f\left(x\right)=\left|\sin x\right|\\ weknowthat-1\le \sin x\le 1forx\in [\frac{-\pi }{2},\frac{\pi }{2}]\\ \Rightarrow 0\le \left|\sin x\right|\le 1forx\in [0,\frac{\pi }{2}]\\ forx\in [0,\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.],f\left(x\right)isone-oneandonto\\ \therefore Domainis[0,\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.]\end{array}$