Also, a circle has radians in it, so any angle + equals that angle.
It's the same as adding 360 degrees, if you do a 360 you are right back where you started, angle x radians + radians = x radians
you can see this by choosing any x value you like, then typing into a calculator sin(x) and (make sure your calculator is in radians and not in degrees)
some suggested values of x that you should try are
i think the identity is proven using the unit circle but i just know it as the addition formula. but also, angel.white is correct, when we are talking about angles in the unit circle, we obtain equivalent angles by adding to the angle, since we just make one complete revolution and come back to where we started.
so for an integer