What makes the radian unit has a better approximation than 360 does?
The radian is a better measure than degrees for angles because:
- It makes you sound more sophisticated if you talk in terms of irrational numbers.
- It allows you to easily calculate the arc length without resorting to trigonometric functions.
(Point 2, is perhaps valid... point 1, no so much).
To a certain extent it is a matter of audience familiarity; where I live, if I were giving directions and told someone to go ahead 100 meters then turn right
My personal idea is that:
The radian unit expresses the measure of an arc's length along the conference. This measure seems very concrete. For example:
The degree reflects the measure of an angle starting from the center of the circle. This measure is of course very abstrait.