One radian is defined as the angle subtended at the centre of a circle by an arc whose length is
- A. equal to the radius
- B. equal to the diameter
- C. equal to the circumference
- D. one metre
Explanation
Since the arc length equals the radius times the angle in radians, an arc of one radius length subtends exactly one radian, about 57.3 degrees. A full circle is therefore 2 pi radians, because the circumference is 2 pi times the radius. Defining the angle this way is what makes the arc length formula and the link between linear and angular quantities so simple.