In calculus and most other branches of mathematics beyond practical geometry, angles are universally measured in radians. This is because radians have a mathematical "naturalness" that leads to a more elegant formulation of a number of important results.
Most notably, results in analysis involving trigonometric functions are simple and elegant when the functions' arguments are expressed in radians.
Although the radian is a unit of measure, it is a dimensionless quantity.
2π radians equals one turn which is 360 degrees.
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