Unit of measure of an angle defined as the measure of a central angle subtended by an arc whose length is equal to the radius of the circle.
In the illustration below, angle BOA measures one radian if arc AB (not the chord AB), is the same length as the radius r.
If arc AB has the same length as the radius, then the length of chord AB a une mesure inférieure au rayon.
Notation
The measure of a radian is written as “rad”, which is read as “radian”.
The system in which an angle is measured in radians is often called the circular system because of the relationship between the radian and the circle.
This diagram illustrates the relationship between the length of the radius of a circle and the radian measure :
- m∠ BOA ≈ 57.3° and m∠ COA = 60°.
- m\(\overline{AO}\) = m\(\overline{OC}\) = m\(\overline{AC}\) = r.
- m\(\overline{AO}\) = m\(\overline{OB}\) = m\(\stackrel{\frown}{AB}\) = r.
As shown in the illustration below, a full angle measures 2π radians or approximately 6.283 rad.
One radian is approximately 57.295°.
