Question

At what points in the interval $[0,2\pi ]$, does the function $\sin 2x$ attain its maximum value?

Answer 1

Maximum value of function $\sin 2x$ is $1$ and that happens when $x=\frac{(2n+1)\pi }{2}${where $n$ is $(0,1,\mathrm{2...})$

So number of places where $\sin \left(2x\right)$ will attain maxima in given domain will be at $x=\frac{\pi }{2},\frac{3\pi }{2}$ i.e. for $n=0$ and $1$.