Use Exercise 66 to prove: f (x) = sin x is the unique solution of Eq. (1) such that f (0) = 0 and f′(0) = 1; and g(x) = cos x is the unique solution such that g(0) = 1 and g′(0) = 0. This result can be used to develop all the properties of the trigonometric functions "analytically"-that is, without reference to triangles.