How do you define the term 'sector' in a circle?

A sector in a circle is a region bounded by two radii and the arc between them.

In more detail, imagine a pizza. When you cut a slice of pizza, you are essentially creating a sector. In mathematical terms, a sector is formed by two radii (plural of radius) of the circle and the arc that lies between them. The radii are straight lines that extend from the centre of the circle to its edge, and the arc is the curved part of the circle's circumference that connects the two radii.

The size of a sector can vary. If the two radii are close together, the sector will be small, like a thin slice of pizza. If the radii are far apart, the sector will be larger, like a big slice of pizza. The angle between the two radii, measured in degrees, determines the size of the sector. This angle is called the central angle.

For example, if the central angle is 90 degrees, the sector is one-quarter of the circle, because 90 degrees is one-quarter of 360 degrees (the total number of degrees in a circle). If the central angle is 180 degrees, the sector is a semicircle, or half of the circle.

Understanding sectors is important in various areas of mathematics, including geometry and trigonometry. They are used to calculate areas and lengths of arcs, which can be useful in real-life applications such as engineering, architecture, and even in everyday tasks like slicing a cake!