Radius

Definition

The radius is the distance from the center of a circle to its perimeter. It is a fundamental measurement that defines the size and shape of a circular object.

5 Must Know Facts For Your Next Test

1. The radius of a circle is half the diameter, and the diameter is twice the radius.
2. The formula for the circumference of a circle is $2\pi r$, where $r$ is the radius.
3. The formula for the area of a circle is $\pi r^2$, where $r$ is the radius.
4. The radius is a key measurement in trigonometric functions, such as sine, cosine, and tangent, which are used to describe the properties of a unit circle.
5. The radius is also an important concept in polar coordinates, where it represents the distance from the origin to a point on the plane.

Review Questions

• Explain how the radius is related to the diameter and circumference of a circle.
  • The radius of a circle is half the diameter, and the diameter is twice the radius. The circumference of a circle is directly proportional to the radius, as shown by the formula $2\pi r$, where $r$ is the radius. This relationship between the radius, diameter, and circumference is fundamental to understanding the properties and measurements of a circle.
• Describe the role of the radius in the unit circle and trigonometric functions.
  • In the context of the unit circle, the radius is always equal to 1. This means that the $x$-coordinate of a point on the unit circle is given by the cosine of the angle, and the $y$-coordinate is given by the sine of the angle. The radius is a key component in the definitions of the trigonometric functions, as it allows for the calculation of the sine, cosine, and tangent of an angle in the unit circle.
• Explain how the radius is used in the formula for the area of a circle and discuss the significance of this relationship.
  • The formula for the area of a circle is $\pi r^2$, where $r$ is the radius. This formula demonstrates the direct relationship between the radius and the area of a circle. The radius is a fundamental measurement that determines the size and scale of a circular object, and understanding this relationship is crucial for calculating the area of circles in various applications, such as in geometry, engineering, and everyday life.

Related terms

Diameter: The diameter of a circle is the length of a straight line segment that passes through the center and connects two points on the circumference.

Circumference:

The circumference of a circle is the distance around the outside of the circle, or the total distance covered by traveling once around the circle.

Arc Length:

The arc length is the distance along the curved part of a circle between two points on the circumference.