Prove that period of function `f(x)=sinx, x in R " is " 2pi.`

Explanation

Let period of `f(x)=sin x " be " T`
` :. F(x+T)=f(x)` for all real x.
or ` sin(x+T)=sin x` for all real x.
` :. Sin(0+T)=sin 0 " " ("putting" x=0)`
` :. T=n pi, n in Z.`
The least value of T is `pi`.
But for `T=pi, sin(x+pi)= -sinx ne f(x)`
So, let `T=2pi` for which `sin(x+2pi)=sinx.`
Thus, period of `sinx` is `2pi`.