Definition:Sector

Definition
A sector of a circle is the area bounded by two radii and an arc.



In the diagram below, $BAC$ is a sector.


 * Sector.png

In fact there are two sectors, together making up the whole of the circle.

When describing a sector by means of its three defining points (as in $BAC$ above), the convention is to report them in the following order:


 * $(1):\quad$ The point on the circumference at the end of the clockwise radius
 * $(2):\quad$ The point at the center of the circle
 * $(3):\quad$ The point on the circumference at the end of the anticlockwise radius

Thus in the sector above, $BAC$ describes the sector indicated by $\theta$, while the sector comprising the rest of the circle is described by $CAB$.

Angle of Sector
The angle of the sector is the angle between the two radii which delimit the sector.

In the above diagram, the angle of the sector $BAC$ is $\theta$.

Again, the conjugate angle of $\theta$ also forms a sector, denoted $CAB$ (see above).