點解radian=2π???

因為冇圖，所以我常試用文字講比你知。

設ＯＣ為一個圓的半徑，

當ＯＣ在旋轉一周後，所旋轉的角度為ａ弧度。

利用公式ｓ＝ｒｂ，其中ｓ＝弧長，ｒ＝半徑，ｂ＝半徑所旋轉的角度（弧度為單位）

圓周　＝　ｒａ

2πｒ　＝　ｒａ

ａ　＝　2πｒ／ｒ

ａ　＝　2π　弧度

所以，３６０度　＝　2π　弧度

2009-09-11 20:26:02 補充：
ｐｓ：弧度只是一種單位

From Wikipedia, you will know that the definition of 1 radian is the angle subtended at the centre of a circle when the arc length = radius of circle.
Since circumference = 2 x pi x r, that means going round one circle, arc length (= circumference) will be 2pi times the radius, that is 2pi radians.
Since angle subtended when going round one circle = 360 degree, therefore, 2pi radians = 360 degree.