i need to prove that sin(x)-x=0 has a unique solution in the open interval (0,pi/2). indicate a computational procedure for finding that solution approximately. on the previous parts of the problem i proved that every contraction mapping is continuous and that every contraction on a complete metric space has a unique fixed pt, so we can use these facts. my intuition is that we'll need to set f(x) = sin x and use the contraction mapping idea, but it's hard to prove that sin x is a contraction mapping. help!!!