Home  18.013A  Chapter 2  Section 2.3 


Derive the formulae for sin x and cos x in terms of exp ix and exp(ix), that follows from equation (A) above.
Solution:
Equation (A) reads
exp ix = cos x + i sin x
and it holds for all x positive or negative, so that we also have
exp(ix) = cos x  i sin x
where we have used the fact that cosine is an even function and sine an odd one.
We can solve these two equations for cos x and sin x
