A radian is a unit of angle that is equal to an angle at the center of the circle in which the arch is equal to the radius.
I would tell someone that a radian is an angle measure around a unit circle.
At about 180 degrees, the radian measure is one pi. At 360 degrees, the radian measure is 2 pi. The circumference of a circle is 2(pi)(r). In the unit circle one time around the circle is 2pi because the radius is 1.
Radians can be converted to degrees and degrees can be converted to radians. They both show a unit of angle measure on the unit circle.
I prefer degrees over radians because I think its easier to determine where it is at on the circle. Radians seem more mathematically pure because instead of using a decimal it will be in a fraction. Fractions are easier to deal with than a decimal. Radians are more precise.
I would tell someone that a radian is an angle measure around a unit circle.
At about 180 degrees, the radian measure is one pi. At 360 degrees, the radian measure is 2 pi. The circumference of a circle is 2(pi)(r). In the unit circle one time around the circle is 2pi because the radius is 1.
Radians can be converted to degrees and degrees can be converted to radians. They both show a unit of angle measure on the unit circle.
I prefer degrees over radians because I think its easier to determine where it is at on the circle. Radians seem more mathematically pure because instead of using a decimal it will be in a fraction. Fractions are easier to deal with than a decimal. Radians are more precise.