Beginning Trigonometry - Lesson 2 - Arc of a Circle

Arc of a Circle

This lesson discusses the equations needed to find the length of the arc in a circle, and calculate its area.

Diagram1

Calculate the length of an arc

To calculate the length of the arc (AB), we take the following equation:

 This can also be summed up as 

(where s = LengthAB)

and refactor it to become:

In english, this means the LengthAB = Radius * theta (angle subtended from the arc - in radians)

Example

If  the radius is 5cm and the sector of AOB subtends and angle of 2 Radians, what is the length of the arc AB?

using our formula , we can work this out to be:

s = 5x2 = 10cm 

Calculate the area of a sector

To calculate the area of a sector using radians and radius. The area of the sector is directly proportional to the angle within the sector.

To calculate the area, the blow equation is used:

area = 

Example

The circle with circle O has a radius of 3, and the sector of AOB subtends and angle of 4 Radians.

Using our formula , we can work this out to be:

which will equal 18cm