the.com/radian
the angle that refuses to play nice with your protractor
means The standard unit of angle in mathematics, equal to the angle subtended at a circle's center by an arc the same length as the radius — roughly 57.3 degrees.
from Built from 'radius' (Latin for the spoke of a wheel or a ray of light) plus the suffix '-an.' The term is a relatively modern coinage in mathematics — it appeared in print in the early 1870s, and the name is generally credited to James Thomson, brother of the physicist Lord Kelvin, who used it in examination questions. The idea fits the word perfectly: the angle is defined by the radius itself, so the spoke names the angle it sweeps out.
definitionarc length equal to the circle's radius
full circleexactly two pi radians, never neatly 360
approximateabout 57.3 degrees, gloriously irrational
calculus loves itderivatives of sine only work in radians
dimensionlesstechnically a ratio, secretly a unit