The Radian corresponds to the ratio of the length of an arc to its radius. More concretely, the measure of 1 radian is the amplitude of an angle to the center of a circle, whose respective arc measures the same as the radius of the circle. In general, mathematicians and physicists prefer to use angle measurement in radians because the calculation formulas are simpler when the independent variable `x` in the trigonometric functions of `sin(x)`, `cos(x)` and `tg(x)` is in radians. The fact that this unit of measure is dimensionless causes that its calculation does not depend on the unit of measure of the length of the arc and the radius. It is thus indifferent that this length is expressed in mm, cm, dm or any other unit of measurement.
The Degree is a measure of the plane angles that corresponds to `1//360` of a circumference. Each degree can be divided into minutes and seconds. The degree has its origin in Babylon, whose system of numbering was based sixty. At that time, it was thought that the Sun revolved around the Earth. Calculations indicated that the Sun took exactly 360 days to complete a full turn. Thus, with each passing day, the Sun ran a part of this path. To this arc, which corresponds to the course of the Sun following its orbit during a day, was made to correspond an angle, whose apex was the center of our planet. This angle became a unit of measure and was called the degree or angle of a degree. Although later, it was shown that it was the Earth that revolved around the Sun and not the other way round, this way of measuring the angles has remained to this day. Another inheritance of the Babylonians is the division of time into hours, minutes, and seconds, which is also done on a similar scale.