III.92 Trigometric Functions by Ben Green: Pages 307 – 308.

Trigometric Functions by Ben Green.

For real or complex z. 

sin(z) = z – z3/3! + z5/5! – z7/7! + …

cos(z) = 1 – z2/2! + z4/4! – z6/6! + …

ez = 1 + z + z2/2! + z3/3! + z4/4! + …

And the coup de grâce:

eiq = cos(q) + i sin(q).

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