Radian is the ratio between the length of an arc and its radius.

Radian is now considered an SI derived unit.

The SI unit of solid angle measurement is the steradian.

The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point.

http://en.wikipedia.org/wiki/Solid_angle

As the ratio of two lengths, the radian is a "pure number" that needs no unit symbol, and in mathematical writing the symbol "rad" is almost always omitted.

An angle of 1 radian results in an arc with a length equal to the radius of the circle.

A complete revolution is 2π radians (shown here with a circle of radius one and circumference 2π).

Advantages of measuring in radians

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. For example, the use of radians leads to the simple limit formula

$\lim_{h\rightarrow 0}\frac{\sin h}{h}=1,$

which is the basis of many other identities in mathematics, including

$\frac{d}{dx} \sin x = \cos x$

http://en.wikipedia.org/wiki/Radian

$\frac{d^2}{dx^2} \sin x = -\sin x.$

Mathematics

Thursday 14 June 2012

Radian