Radian symbol, and in mathematical writing the symbol "rad" is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and when degrees are meant the symbol ° is used. It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or , or 2. Thus 2 radians is equal to 360 degrees, meaning that one radian is equal to 180/ degrees. The relation formula_1 can be derived using the formula for arc length. Taking the formula for arc length, or formula_2.
Degree (angle) this system. In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2"" radians, so 180° is equal to radians, or equivalently, the degree is a mathematical constant: 1° = . The turn (or revolution, full circle, full rotation, cycle) is used in technology and science. One turn is equal to 360°.