TITLE: Why do we use radians for polar coordinates rather than degrees?
QUESTION [25 upvotes]: Is there a specific reason why radians must be used when converting from Cartesian to Polar coordinates, is it just a convention or does it not matter at all?

REPLY [2 votes]: As many others commented, radians are the natural unit.
Degrees exist only for historical reasons and are not an extremely practical unit (not mentioning the minutes/seconds issue). One of their only assets is that $360$ is divisible by $2,3,4,5,6,8,9,10$ and others.

IMO, we are lacking a truly practical unit, which does not involve the constant $2\pi$: revolutions, i.e. a full turn corresponding to $1$ unit.