How do I show that $\cos(x)$ is a contraction mapping on $[0,\pi]$? I would normally use the mean value theorem and find $\max|-\sin(x)|$ on $(0,\pi)$ but I dont think this will work here.
So I think I need to look at $|\cos(x)-\cos(y)|$ but I can't see what to do to get this of the form $|\cos(x)-\cos(y)|\leq\alpha|x-y|$?
Thanks for any help