Consider the function sin( \pi x) on [-1,1] and its approximations by interpolating polynomials. For integer n \geq1, let x_{n,j}=-1+\frac{2j}{n} for j=0,1,...,n, and let p_{n}(x) be the nth-degree polynomial interpolating sin( \pi x) at the nodes x_{n,0},...,x_{n,n}. Prove that

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