What are radians?

Angle measurement

The word trigonometry comes from Greek roots that loosely translate to the “measure of triangles.” Most folks are familiar with using degrees to measures. Measurements of angles can be measured in degrees or radians. Converting between the two units of measurement is analogous to converting between other forms of measurement units.

Radians reflect the length of an angle’s corresponding arc created by the unit circle.

 

 

unit circle

By Gustavb (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons

If we recall the unit circle has a radius of 1. The circumference of a circle is given by the formula:2?radius. Since the radius of a unit circle is 1, the radius of the unit circle is 2?. The equivalent measurement in degrees is 360°.

Radians can be thought of as rotations from the x-axis, starting at the portion of the cartesian coordinate plane where the x-axis is positive and rotating counterclockwise. When we rotate to 90°, the equivalent measurement in radians is ?/2; when we rotate to 180° the equivalent measurement is ?; when we rotate to 270° the equivalent measurement is 3?/2, and the full 360° rotation is equivalent to 2?.

radian animation