What Are Radians? (Mathematics Lesson)
What Are Radians?Radians are a unit of measurement of an angle.
There are 2π radians in a full rotation.
Definition of a Radian1 radian is the angle found when the radius is wrapped around the circle.
More generally, the angle in radians is equal to:
Important Angles in Radians
NoteWHAT IS AN ANGLE?
An angle is a measure of the rotation between two straight lines that share a common endpoint.
WHY ARE THERE 2π RADIANS IN A CIRCLE?
The angle in radians is the arc length divided by the radius.
For a full circle, the arc length is the circumference.
The circumference of a circle with a radius of r is 2πr.
This is why the full angle in radians is 2π radians.
IMPORTANT ANGLES IN RADIANSThe important angles in radians can be found by proportion with a whole circle.
A right angle is a quarter of a full angle.
¼ × 2π = π ⁄ 2 radians.
A straight angle is a half of a full angle.
½ × 2π = π radians.
Three quarters of a rotation is three quarters of a full angle.
¾ × 2π = 3π ⁄ 2 radians.
OTHER MEASURES OF ANGLESThe degree is another measure of angles.
There are 360 degrees in one rotation.
Degrees are denoted by the symbol °.
Read more about degrees