Find the regions where sinx < x
Maybe this will help.
I took this image from http://webgraphing.com/
sinx is always between -1 and 1. It follows then, that when |x|>1, the graph will either become more and more negative, or more and more positive. Know that, all you must do is analyze the behavior of the graph for -1<x<1 and determine the behavior of the function for those values.