Trigonometric Functions: Basic Angles and Radian Measures

Radians and Degrees

There are two ways to measure angles, radians and degrees.

A measure of 360° is equivalent to two times pi radians and is the measure of a full rotation around a circle. Θ is the measure of this angle.

Circle with full rotation of three hundred sixty degrees or two pi radians

If you divide the circle into smaller angles the degrees and radian measures of θ change.

Circle with 360 degrees or 2 pi radians, 90 degrees or pi over two radians, 180 degrees or pi radians, and two hundred seventy degrees or three pi over two radians.

Notice that the angles are positive when they are created in the counterclockwise direction. They can also be created in the clockwise direction which produces a negative angle. The blue angle is equal to -90° or negative pie divided by 2 .

The circle can then be subdivided into even smaller angles. We will discuss this further along in this section.