What is one radian defined as?

One radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. When you take a circle and look at two radii that form an angle at the center, if the arc length of the circle between those two radii is the same as the radius, then that angle is one radian. This means that the measurement of the angle directly relates to the radius and the arc length of the circle, making it a unique and fundamental unit in both mathematics and engineering, especially when dealing with circular motion and trigonometry.

The concept of radians is crucial because it provides a natural way to measure angles that is consistent with the geometry of circles, unlike other methods such as degrees, which do not have this direct relationship with the circle's properties. Understanding this definition is important as it plays a significant role in various calculations and formulas used in power engineering.