How to find the period of this trigonometric function

Question

$y$ = $|\sin x|$

I know the period is π by drawing the graph, but I can't prove it. Please use this method we have learnt for other functions. For example

$y=\sin2x$

$\sin2x= \sin2(x+T)$

$2x+2π=2x+2T$

$T=π$

Answer 1

As $\cos2x=1-2\sin^2x,|\sin x|=+\sqrt{\dfrac{1-\cos2x}2}$

$|\sin x|$ has one-one correspondence with $\cos2x$

Now $\cos2(x+T)=\cos2x\iff2\sin T\cos(2x+T)=0$

Can you take it from here?