TITLE: Why are turns not used as the default angle measure?
QUESTION [28 upvotes]: Why is $2\pi$ radians not replaced by $1$ turn in formulas?
The majority of them would be simpler. If such a replacement was proposed earlier, why was it declined?

REPLY [3 votes]: Just a complement to zahbaz answer.
With angles in radian, you get the nice formulas:
sin' = cos
cos' = -sin

sin(x) = 1/2 * (exp(ix) - exp(-ix))
cos(x) = 1/2 * (exp(ix) + exp(-ix))

Of course those are mathematical considerations, and that's the reason why in common life we use degrees.
But there are other units. In artillery, the thousandth (millième in french) is used. You have 6400 of then in one turn (why not...) but as an approximation, it gives an elevation of 1m at 1km of distance. If you have this in binoculars and can guess the height of something, you can easily compute a distance - even a military can...