For most of your school years, you’ve worked in degrees. Then suddenly, in Precalculus, you are hit with radian measure and the Unit Circle. If you had started learning about radian measure in Geometry, you wouldn’t be so freaked out by it!

Circle divided into 1, 2, and 3 radian sectors

This is the deal:

Radians measure is defined by two aspects of a central angle: the length of the intercepted arc and the radius of the circle.

If the arc length is equal to the radius, the central angle is 1 radian. If the arc length is twice the radius, the central angle is 2 radians. Etc. That’s it!

Where does all the pi stuff come in?  Well, check out the total radian measure of this circle. Does that number seem familiar?