A radian is a unit of measurement on a circle that is equal to the radius. The formula for circumference of a circle is 2(pi)(r). On the unit circle, pi radians is one half the way around the circle. 2pi is the full circle. This is because the radius times pi is equal to half of the circumference of the circle. In terms of degrees, a radian is about 57.2958. The radian is if you took the length of the radius, put it on the outline of the circle, then created a triangle of sorts with those lengths. I prefer to use radians when doing things involving the unit circle or graphing the unit circle, but degrees are preferable when looking at arc length or other things because they are more natural to me.
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