How to know if a function is periodic

If you know the sine function, graph it.

You will notice that this graph begins at (0,0) and ends at (2pi, 0). It then repeats itself indefinitely. This is one concrete example of a periodic function.

The cosine function cos x is another periodic function. Its graph begins at (0,1) and ends at (2pi, 1). The graph then repeats itself indefinitely.