In math, there are two different systems for measuring angles: the degree angle system and the radian angle system. While the degree angle system is often used to introduce the concept of angles, the radian angle system is the preferred angle system in math.
Using radians leads to more succinct and elegant formulas throughout math. For example, in calculus, the derivative of the sine function is simpler when the angle is expressed in radians.
If the sine function was instead defined in terms of degrees, let’s call this version , then taking the derivative would result in an extra factor in front of the degrees version of the cosine function.
The radian angle system is a unit of measure for angles. To measure an angle in radians, divide the arc length of the angle by the radius used to draw the arc. A full rotation is equal to 2π radians.
Degrees are a unit of measure for angles. A full rotation is equal to 360 degrees. In the XY Cartesian Coordinate System, degrees are measured starting from the rightmost edge of the circle.