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 57.3^(∘).

If the arc length is 2 radii, the measure of the corresponding central angle is 2 radians, and so on. Therefore, radians describe the number of radii an angle creates on a circle.

It can be observed that a semicircle corresponds to an arc length of π radii and the circumference of a circle corresponds to an arc length of 2π radii.

Measured in degrees, a semicircle is equal to 180^(∘). Therefore, π radians and 180^(∘) correspond to the same angle measure. 180^(∘)=π rad 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. cos 64^(∘) and cos 5 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.