Why is the implementation of computing both sine and cosine at the same time about the same speed as just computing one of them?

Question

Was messing around with C and found this quirk. How does this function work so quickly? How is it implemented?

In: Mathematics

Answer 1

Most implementations use a Taylor series expansion (cos = 1 – x^2 /2! + x^4 /4! – x^6 /6! …, sin = x – x^3 /3! + x^5 /5! – …) or lookup table. Cos and Sin are the same, just pi/2 out of phase, so you only need to do it once.