If is such that for all values of then is periodic with period . This means that the graph repeats every units horizontally.
To find where , we need to know where the graph crosses the -axis. Between and , the graph cuts the -axis times; so it will cut it another times between and . (That's so far.)
Between and , the graph crosses the -axis just once; so it will cross once between and .
So there are values of between and altogether.