The equivalent if sin taking revolutions (let’s say sinr) is just sinr(x)=sin(x
2pi) there is no fundamental mathematical relation broken by this, that would indicate math was broken at the core. And the Taylor expansion isn’t any less simple, you simply state the pi’s in the expansion rather than having them implied in your input variable.
It’s amazing people assume math will break somehow if you use a different unit for angles, when most should at least be familiar with using both 360 and ~6.283 and some using 200 as the scale for one rotation. And when trying to reason about it every single person always translates this into ratios of rotations or percentages of rotations.