Signal is periodic or not

Hello
I understand that signal is periodic if it repeat after fixed time
Look at example

I know the signal is periodic because it repeat after 2pi period. 2pi,4pi,6pi.....20pi
How to find out that signal is periodic or not?

It's periodic if it continues foreever with the same pattern.

crutschow said:

It's periodic if it continues foreever with the same pattern.

Click to expand...

Yes I agree but how to find out using example. So I tried with example. I know the condition for periodic signal but I really don't understand the logic behind condition