A Periodic Function
$ x(t) = sin(t) $
Clearly, $ x(t) $ is periodic because there is a $ T > 0 $ such that $ x(t + T) = x(t) $ for all $ t $. An obvious choice for $ T $ would be $ T = 2\pi $. Shifting $ x(t) $ by $ 2\pi $ gives the original function since $ 2\pi $ is the fundamental period of $ x(t) = sin(t) $
