Suppose that F is a function that is continuous at all points in the interval [0,1]. Suppose also that for all b<1 there is some x such that 0x1 and sin(f(x))>b. Prove that there is some point z in the interval [0,1] such that sin(F(z)) = 1. Your proof must quote all relevant theorems from the text and show that their hypotheses are satisfied.