Home | 18.013A | Chapter 2 | Section 2.3 |
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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 =Â cos x + i sin x
and it holds for all x positive or negative, so that we also have
exp(-ix) =Â 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
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