Indeed, this is what Pico-8 uses for its trigonometric functions[1] (angles go from 0 to 1, instead of from 0 to 2*Pi). I was surprised by this at first, but then I found it is very convenient and simplifies a bunch of stuff.

http://pico8wiki.com/index.php?title=Sin

I think it misses the whole point of Pi. Turns are for angles. Pi is not a measure of angle. It is a number that can be used to find the length of an arc. For example, it gives half-length of an arc, given an angle in Turns. So it deals with lengths, not strictly angles. Turns deal with angles only.

Maybe related

Hamilton's theory of turns revisited

https://arxiv.org/abs/0904.4787

I'm not super versed on the subject, but I think there's a case where using radians allows you to do direct multiplication without any conversion when trig isn't even involved, for rotation or transformation matrices? In which case this would fall apart rather completely if that doesn't work anymore and wouldn't be any different than switching to degrees, a convenience fix that requires conversion anyway.

Wait until you discover gradians: centesimal system applied to angles. A turn is 400 gradians, right angles are 100 gradians.

Same advantages as here but multiplied times 400...

The title should say (2022)

It's similar to why taxicab distance is better for distance measurement on limited hardware where sqrt() costs precious cycles. The reason to use sin() though is because it's a lookup table (where it counts) and not a bit of math, so moving to turns isn't necessarily a win.

At least we got metric units out of the French Revolution.

Gradians exist because "let's change everything, even things that aren't broken".

Norman Wildberger has an alternative system for trigonomtry:

Understanding uniform motion: are radians really necessary? | WildTrig

https://youtu.be/CnQXRdgN_7I?si=EiYY99i6mBOIyczI

Wild Trig: An introduction to Rational Trigonometry

https://youtube.com/playlist?list=PLIljB45xT85CyF_7bKd6y36VA...

Turn is a measurement unit, and measurement units are just numbers. So turn ≈ 6.28318530718. You're welcome.

That should put to bed that whole τ crap. "But the symbol τ is used for other things!" Yeah, yeah, yeah, just write turn. Even better, because it's more international and has more precedent, write rev for revolution.