Circumference

Definition

The circumference is the distance around the edge of a circle. It can be calculated using the formula $C = 2\pi r$ or $C = \pi d$, where $r$ is the radius and $d$ is the diameter.

5 Must Know Facts For Your Next Test

1. Circumference is directly proportional to both the radius and diameter of a circle.
2. The unit circle has a circumference of $2\pi$ because its radius is 1.
3. In trigonometry, understanding circumference helps in defining periodic functions like sine and cosine.
4. The relationship between arc length and circumference can be used to determine angles in radians.
5. Knowing the circumference allows for conversion between radians and degrees, since $360^{\circ}$ corresponds to a full circle.

Review Questions

• What are the formulas used to calculate the circumference of a circle?
• How does knowing the circumference help in understanding sine and cosine functions?
• Why is the unit circle's circumference equal to $2\pi$?

Related terms

Radius: The distance from the center of a circle to any point on its edge.

Diameter: A straight line passing through the center of a circle, connecting two points on its edge. It is twice the length of the radius.

Unit Circle: A circle with a radius of one, centered at the origin of a coordinate plane, used frequently in trigonometry.