Radian measure

Definition

Radian measure is a way of measuring angles based on the radius of a circle. An angle in radians is defined as the ratio of the length of the arc to the radius of the circle.

5 Must Know Facts For Your Next Test

1. The radian measure of a full circle is $2\pi$ radians.
2. There are $\pi$ radians in 180 degrees, making the conversion factor $\pi/180$.
3. One radian is approximately 57.3 degrees.
4. Radians are dimensionless because they represent a ratio.
5. Common angles in radians include $\pi/6$, $\pi/4$, $\pi/3$, and $\pi/2$.

Review Questions

• What is the radian measure for an angle of 90 degrees?
• How do you convert an angle from degrees to radians?
• Why are radians considered dimensionless?

Related terms

Unit Circle: A circle with a radius of one, centered at the origin, used to define trigonometric functions.

Arc Length: The distance along the curved line forming part of the circumference of a circle.

\( \theta \): A variable commonly used to represent an angle in mathematics.