Radian Measure

The radian is a unit of angle measure used in mathematics. It offers an alternative to degrees and is particularly useful in calculus, trigonometry, and complex number theory.
Formally, a radian is the angle subtended by an arc of a circle that has a length equal to the radius of the circle.
To give an idea of the size, one radian is approximately 57.3 degrees.
There are approximately 6.28 (or 2π) radians in a full circle. This comes from the fact that the circumference of a circle is 2π times its radius.
Radians and degrees can be converted using the relation 180 degrees = π radians.

Using Radian measure

Many mathematical functions are more naturally defined in terms of radians. For example, the functions for sine, cosine and tangent are typically taught first using degrees, but they are more fundamentally related to radian measure.
Hence, most calculators and computing systems use radians by default when calculating angles in trigonometric functions.
In physics and engineering, radian measure is commonly used for angle measurements because it simplifies certain formulas.

Radian measure comes up naturally in many areas of mathematics and science. It is a fundamental concept that helps bridge different areas of maths such as geometry, trigonometry, calculus, and complex number theory.
A good understanding of radian measure is important for understanding how circular motion and waves are modelled in maths and physics.
Remember, although it might seem more tedious than using degrees, radian measure provides a way to make complex mathematical ideas simpler and more elegant.