There's this sine approximation (mentioned in title) which works over the interval $[0, \pi]$: $$ \sin x \approx \frac{16x(\pi-x)} {5\pi^2-4x(\pi-x)} $$ With little changes it can be put work over the interval $[-\pi, 0]$: $$ \sin x \approx \frac{-16x(-\pi-x)} {5\pi^2-4x(-\pi-x)} $$ Approximation results as - https://www.desmos.com/calculator/cvoewagqer
Is there any change to join these two formulas into one equation to work in range $[-\pi, \pi]$? If there's ... how?
Source: P.Giblin's paper: https://www.liverpool.ac.uk/~pjgiblin/papers/sine-approx.pdf
How about $$ \sin x = (\text{sgn}(x) 16x(\text{sgn}(x)\pi-x) / 5\pi^2-4x(\text{sgn}(x)\pi-x))$$
(*This is purely based on the formulae given.)