Interpolating polynomial for sin($\pi{x}$)

1. Dec 7, 2011

alphabeta89

1. The problem statement, all variables and given/known data
Consider the function sin($\pi$$x$) on [-1,1] and its approximations by interpolating polynomials. For integer $n$$\geq$1, let $x_{n,j}=-1+\frac{2j}{n}$ for $j=0,1,...,n$, and let $p_{n}(x)$ be the $n$th-degree polynomial interpolating sin($\pi$$x$) at the nodes $x_{n,0},...,x_{n,n}$. Prove that

$\max_{x\in[-1,1]}\left | {sin}{(\pi{x})-p_{n}{(x)}} \right | \to 0$ as $n \to \infty$

2. Relevant equations

3. The attempt at a solution
I have no idea how to start!!!