Unit Circle Radians

The unit circle is labeled using the radian angle system, because the unit circle visualizes the output of the trigononometric functions and the trigonometric functions use radian angles as input. While degrees are sometimes also included, radians are the preferred unit for measuring angles in math[1].

Radians Overview

Radians measure angle as the ratio of the angle’s arc-length over the radius of a circle. A full rotation in radians is equal to (tau) radians. Since the unit circle has a radius , angles measured in radians on the unit circle have the unique property that their arc-length is equal to their measured value. The interactive above visualizes a full rotation in radians.

Example Angles

The two charts below show common angles measured in radians on the unit circle and their corresponding points. The angles on the first chart are formed by dividing the unit circle into equal parts.

The Unit Circle Divided by 8 measured using the circle constant.
Figure 1: Unit Circle Chart Eighths τ (tau)

The angles on the second chart are formed by dividing the unit circle into equal parts.

The Unit Circle Divided by 12 measured using the circle constant.
Figure 2: Unit Circle Chart Twelfths τ (tau)

References

  1. Radians Versus Degrees
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