What is the best approximation for sine?

Question

Can you tell me which is the best approximation for cosine/sine functions. It should also reduce the computational complexity. I've already tried the Bhaskara I's approximation.

Can you suggest me anything better?

Thanks in advance.

Answer 1

For $-\pi\le x \le \pi $ I found $$\left(\frac{315}{2}\pi^2 - \frac{15}{2\pi^2} \right)x + \frac{175}{2\pi^6}\left( \frac{\pi^2}{5}-3\right)x^3,$$ is it of any help?

Answer 2

Hopefully you're interested in the following double inequality, valid for $0\le x\le\pi$: $$x\left(1-\frac{x}{\pi}\right)\le\sin x\le \frac{4x}{\pi}\left(1-\frac{x}{\pi}\right) $$