Radians and circular regions

A radius joins the centre of a circle to its circumference. A chord joins two points on the circumference; an arc is part of the circumference.

Sector and segment

A sector is bounded by two radii and an arc. A segment is bounded by a chord and an arc. A minor region is the smaller of the two regions of the same kind; a major region is the larger.

The shaded region above is a minor sector.

The shaded region above is a minor segment. The dashed radii help identify the angle at the centre.

Radian measure

An angle of one radian subtends an arc equal in length to the radius. In general, \(\theta=\dfrac{l}{r}\), where \(l\) and \(r\) use the same length unit.

A full turn is \(2\pi\) radians, so \(180^\circ=\pi\) radians.

For example, \(120^\circ=\dfrac{2\pi}{3}\) radians and \(\dfrac{3\pi}{4}\) radians \(=135^\circ\).