[mathematical notes] radian

radian

Radian is horn Unit of measure .

1 The angle of radian ： radius = Arc length

Definition ：

         Arc length be equal to radius Arc of , The center angle of the circle it faces is 1 radian .

 

The formula ：

• radian = Arc length / radius
• Arc length = radian * radius

degree ——> radian

        radian = （ angle  / 180）* π

radian ——> degree

        degree = radian *180/π

Derivation process ：

         because ： The circumference of a circle  = 360 Arc length of degree angle ;

                    The circumference of a circle = 2πr ;

         therefore ：360 Angular Arc length =  2πr;

        Again because ： radian = Arc length / radius   

        therefore ：  radian （360 degree ）= 2πr / r = 2π 

                      radian （180 degree ） = π 

therefore ：： radian （θ Degree angle ）= （ θ / 180）* π

Common conversion

angle	radian
360	2π
180	π
1	π / 180
θ	θ * π / 180

radian	angle
π	180
1	180 / π
X	X * 180 / π