Comment by srean

A notable approximation of ~650 AD vintage, by Bhaskara is

   ArcCos(x)= Π √((1-x)/(4+x)).

The search for better and better approximations led Indian mathematicians to independently develop branches of differential and integral calculus.

This tradition came to its own as Madhava school of mathematics from Kerala. https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and...

Note the approximation is for 0 < x < 1. For the range [-1, 0] Bhaskara used symmetry.

If I remember correctly, Aryabhatta had derived a rational approximation about a hundred years before this.

EDIT https://doi.org/10.4169/math.mag.84.2.098