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Re(exp(ix)).

Using degrees, turns, etc instead of radians, is like using 10^y instead of e^x (where y=x/ln(10)). Useful for many practical things, but useless for a lot of math applications, especially involving differential equations, complex numbers etc.

Right - there's a negotiation in terms of complexity. The coefficient baggage has to go somewhere.

For me I don't want to care which units I use (and I'm rarely inspecting the exact angle as a number) - consistency is most important. I'm rarely interested in the precise numerical value of an angle - it's just a thing in the graphics/physics pipeline somewhere.

I don't know if that makes me agnostic about this proposal or conservative.

When you store a value that will be reused, like in an array of points, if every time you walk the array multiplying by a constant, you should seek to store values in such a way that it does not need that treatment. If you are taking sin and cos each time through (presumably, added to some angle), it should be pre-multiplied for the fastest implementation of sin and cos available.

> and the derivative of sin(x) is ... ?

I believe it's cos(x). And I fail to see how that would change regardless of what unit x is expressed in. Sorry, my trig is veeery rusty.

Only when the angle is in radians ...