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 Radian
1 radian is the angle found when the radius is wrapped around the circle.More generally, the angle in radians is equal to:
- the arc length divided by the radius.
- arc length of a circle with radius 1 (the unit circle).
Important Angles in Radians
- ^{π} ⁄ _{2} is a right angle, a quarter of a rotation.
- π is a straight angle, a half of a rotation.
- ^{3π} ⁄ _{2} is three quarters of a rotation.
- 2π is a full angle, a whole rotation.
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Interactive Test
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WHAT 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 RADIANS
The 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 ANGLES
The degree is another measure of angles.There are 360 degrees in one rotation.
Degrees are denoted by the symbol °.
Read more about degrees