📂Geometry

Radian

Definition

The angle of a sector with a radius $r$ and an arc length $\ell$ is called $\theta$ $\text{rad}$. Here, $\text{rad}$ is read as radian.

Explanation

Since it is a value derived from dividing a length by a length, it is a dimensionless unit. Therefore, this unit is often omitted in usage. An angle without a unit is fundamentally assumed to be in radians. In the unit circle, where the radius is $1$, the radian value equals the arc length. Hence, it can be understood that the circumference of the unit circle $2\pi$ corresponds to $360^{\circ}$. The relationship with degrees is as follows.

$$1 \text{rad} = \dfrac{180^{\circ}}{\pi} \approx = 57.2958^{\circ}$$

$$1^{\circ} = \dfrac{\pi}{180} \text{rad} \approx 0.0175 \text{rad}$$