Definition of the Radian Measure

 

The radian measure is an angle measure in which an angle of 1 radian is counted as one. In other words, the radian measure of any angle is the ratio of this angle to the radian.

The definition of the radian measure implies that the magnitude of the round angle equals 2π radians.

There is also another way to determine the radian measure: the radian measure of an angle is the ratio of the arc length of the circle between the angle sides to the radius of this circle when the center of the circle coincides with the angle’s vertex.

 

 

Formula of the Radian Measure of an angle

 

The Radian Length of angle α can be determined as follows:

When rotated in the positive direction:

Radian Measure

When rotated in the negative direction:

Radian Measure

Radian Measure of angles

Radian Measure of angles. Definition

Radian Measure in trigonometry

 

In trigonometry, a unit circle with the center in the angle vertex is used to find the radian length of an angle; then, the radian length of the angle equals the arc length of the unit circle between the angle sides.

When rotated in the positive direction:

Radian Length in trigonometry

When rotated in the negative direction:

Radian Length in trigonometry

Radian Length in trigonometry

Radian Length in trigonometry