The period of an function, is how many times it takes to complete one cycle, if the period is 2π then after 2π the function would have been completed one entire cycle, but what I mean by cycle?
It's when the function start again, these functions are called periodic functions for a reason, after between that interval, the function goes up, goes to 0 again, go down and finally goes zero again, it means a cycle! the function goes up, down and then return to the same point.
If you look at the picture, the function took 2π just to go up and zero, it needs more 2π to go down and return to zero, then it's period is 4π.
The bottom function complete its cycle in just π!
I hope you liked it, maybe the draw will help you!
Any doubt? just write in the comment and I'll help you.
