Question: Use Exercise 66 to prove: f (x) = sin x is the unique solution of Eq. (1) such that f (0) = 0 and f(0)

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.

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f x sin x satisfies Eq 1 and we can directly calculate that f 0 sin 0 0 and f0 cos 0 1 ... View full answer

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