Radian

Definition

A radian is a unit of angular measure where the angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution around a circle is $2\pi$ radians.

5 Must Know Facts For Your Next Test

1. There are $2\pi$ radians in a full circle, equivalent to 360 degrees.
2. To convert degrees to radians, multiply by $\frac{\pi}{180}$.
3. To convert radians to degrees, multiply by $\frac{180}{\pi}$.
4. An angle of $\pi$ radians corresponds to 180 degrees.
5. The unit circle uses radians to define angles for sine and cosine functions.

Review Questions

• How many radians are there in a full circle?
• Convert an angle of 90 degrees to radians.
• What is the radian measure for an angle that corresponds to one-quarter of a circle?

Related terms

Unit Circle: A circle with a radius of one centered at the origin, used in trigonometry to define sine and cosine functions.

$\pi$ (Pi): A mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.

Degree: A unit of angular measurement where one full revolution equals 360 degrees.