1 radius......wrapped around a circle.............would be approx. 1/6 of it..................

Example: How Many Radians in a Full Circle?

Imagine you cut up pieces of string exactly the length from the center to the circumference of a circle ...
... how many pieces do you need to go once around the circle?

Answer: 2π (or about 6.283 pieces of string).

Radians Preferred by Mathematicians

Because the radian is based on the pure idea of "the radius being laid along the circumference", it often gives simple and natural results when used in mathematics.
For example, look at the sine function for very small values:

x (radians)	1	0.1	0.01	0.001
sin(x)	0.8414710	0.0998334	0.0099998	0.0009999998

For very small values. "x" and "sin(x)" are almost the same
(as long as "x" is in Radians!)