I am thinking that programming languages should make cycles the standard angular unit. It is the most convenient for programming. It is less baffling to normal people than radians. Computers can express them exactly.
Mathematicians may still have reason to prefer radians, but they are smart enough to know how to do the conversion.
Most people measure angles in degrees (0 ... 360). Most mathematicians measure angles in radians (0 ... 2π). But as a programmer, I think it is best to measure in cycles (0 ... 1). It is trivial to correct overrotation (discard the integer part). It is trivial to find the quadrant (the two msbs). Table look implementations of sine are trivial as well.
All three conventions work, and each is easily convertible into the others.
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