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Concept

Radian

A radian, like a degree, is an angle unit. One radian is defined as the measure of the central angle that intercepts an arc equal in length to the radius of the circle. It corresponds to roughly
Animation of forming an arc that measures 1 radian
If the arc length is radii, the measure of the corresponding central angle is radians, and so on. Therefore, radians describe the number of radii an angle creates on a circle.
Rotation of a point on a circle
It can be observed that a semicircle corresponds to an arc length of radii and the circumference of a circle corresponds to an arc length of radii.
Rotation of a circle along a segment
Measured in degrees, a semicircle is equal to Therefore, radians and correspond to the same angle measure.
By using this relation, degrees can be converted into radians and vice versa. In calculations, even if the angle is given in radians, rad is seldom written. Instead, no unit marker indicates radians. Consider two expressions.
The first angle is given in degrees, and the other is given in radians. At first glance, radians might seem inconvenient, but they make calculations simpler in certain circumstances, like derivatives and integration. Radians are also the SI unit for angles.