Functional Form of this curve

Question

I'm trying to describe this graph in a functional form. My apologies for the quality of the drawing. It is meant to be a depiction of a sine wave which reaches its maxima, the gradient of the graph then goes to $0$ for a period of $x$ equal to that of the domain of the sine wave. It then increases by the sine wave again and this process repeats itself throughout the function domain.

Thank you for your help.

Answer 1

For example, $\,f(x)=x-\sin(x)\,$ is monotonically increasing, with inflection points at $\,x=2k\pi\,$.