I need to show f:[0,1]->[0,1] is a contraction mapping. where g is continous map form [0,1] to itself

When I try |f(x)-f(y)|, using triangle inequality and sinx<1, I get it is less that or equal to which I can't seem to manipulate (even aware that x,f(x) are in [0,1]) to k|x-y| as required.