# Order of convergence of the Newton-Raphson method

Given $f(x) = x - sin(x)$, I'm asked to solve this using the Newton-Raphson method and give the order of convergence. Now for me this is strange because I need to have a starting value $x_0$ in order to go through the Newton-Raphson method.

However, I really don't know how to calculate the order of convergence. Any help for this formula, and how to do this in general?

The only root is $x=0$ and it has multiplicity $3$. Now apply what you know about the convergence of Newtons method to multiple roots.