4.2-Degrees and Radians

Radians and degrees are two units for measuring angles.

Degrees

Degrees are used to measure direction and angle size. If you are facing north, you are said to be at 0°. If you turn the opposite direction to face south, you have turned 180°.

A full circle is comprised of 360°. 

Radians

The formal definition of a radian is that a radian is the measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle. The radian measure for a full circle is 2π. This might look even messier than 360°, but if you follow through on the math, it actually works out. If you remember, the equation for finding the circumference (C) of a circle with radius (r) is C = 2πr. If r = 1, then C = 2π. FIr this reason, 2π is equal to one full revolution around a circle or 360°A circle with a radius of 1 is called a Unit Circle.

Some examples