Find the regions where sinx is less than or equal to x

The range of sin(x) is -1 to +1. Obviously, any x greater than or equal to +1 is in the region and every x < -1 is outside the region. The question left to answer must be strictly for -1 < x < +1.

sin(x) < x
or
x - sin(x) > 0 (equation 1)

If you graph the shape of the sine curve, you'll see that equation 1 holds (with -1 < x < 1) for all x > 0 and fails for all x < 0.