In a unit circle, the radian measure of the central angle is equal to the length of the arc that it subtends on the circle. A unit circle is defined as a circle with a radius of one unit, typically centered at the origin of a coordinate system.
When you measure an angle in radians, you’re essentially measuring the angle based on the corresponding arc length on the unit circle. For example, if the central angle measures 1 radian, the length of the arc formed by that angle is also 1 unit. This relationship is fundamental in circular motion and trigonometry, as it directly connects angular measures and linear distances along the circle.