Doom also uses the famous fast inverse square root method which although I know how it works still amazes me.
It doesn't, to the best of my knowledge. It appeared in an id game for the first time in Quake 3.
Julia?
Julia uses a very similar approach to musl here. Reduction mod 2pi followed by polynomial kernel. We use tables for `exp` and `log`, but the trig functions have good reductions so we use those instead. The implementation is here https://github.com/JuliaLang/julia/blob/03af78108afe6058f54c... for anyone interested.
In the Julia repl, just type '@less sin(pi)' to view the source code of sin. I don't know of any other programming language that makes it this easy to look at its internals.
That's how we nerd snipe people into contributing to Base (only 10% joking).