A sector's area can be calculated using the formula $A = \frac{1}{2} r^2 \theta$, where $r$ is the radius and $\theta$ is the central angle in radians.
The length of the arc (s) forming part of the sector is given by $s = r \theta$.
When $\theta$ is measured in degrees, you must convert it to radians first for calculations involving trigonometric functions.
A sector with a central angle of $360^{\circ}$ forms a complete circle.
Sectors are used to model real-world problems, such as portions of circular tracks or slices in pie charts.
Review Questions
What is the formula for calculating the area of a sector when the radius and central angle are known?
How does one convert an angle from degrees to radians?
If a sector has a central angle of $180^{\circ}$, what fraction of the circle does it represent?
Related terms
Central Angle: An angle whose vertex is at the center of a circle and whose sides are radii.
Arc Length: The distance along the curved line forming part of the circumference of a circle.
Radians: A unit for measuring angles based on the radius of a circle; one radian equals about 57.3 degrees.