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[mathematical notes] radian
2022-07-07 07:44:00 【Porridge cook_ ninety-nine】
radian
Radian is horn Unit of measure .
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 |
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