how to find the period of a function?

For a periodic function i.e., functions which repeat over a cycle in a specific period its fundamental period is defined as the length of a smallest continuous portion of the domain over which the function completes a cycle

Example:

For the function y = sin x

Its fundamental period is 2π
 f(x)=sin x, we notice that f(x) starts repeating its values from  2n$\mathrm{\pi }$ to2(n+1)$\mathrm{\pi }$ So the fundamental period of the function will be  2(n+1)$\mathrm{\pi }$ -2n$\mathrm{\pi }$ = 2$\mathrm{\pi }$ .2nπ to 2(n+1)So, the fundamental period of the function f(x)=sin x is =2(n+1)π−2nπ=2π.