Radians
The angle subtended at the centre of an arc equal in length to the radius is 1 radian
\[ \pi \text{ rad} = 180^\circ \]
Interactive – Radians Interactive CAST DiagramProof
Convert to radians
\[ 180^\circ = \pi \text{ rads} \qquad \text{Divide degrees by } 180^\circ \text{, then multiply by } \pi \text{ rads.} \]
Examples
Convert to degrees
\[
\pi \text{ rads} = 180^\circ
\qquad
\text{Multiply rads by } 180^\circ \text{, then divide by } \pi.
\]
Examples
Exact values
In degrees
In radians
Using exact values
Quadrant 2
180° − 30° = 150°
180° − 45° = 135°
180° − 60° = 120°
π − π/6 = 5π/6 rads
π − π/4 = 3π/4 rads
π − π/3 = 2π/3 rads
Quadrant 3
180° + 30° = 210°
180° + 45° = 225°
180° + 60° = 240°
π + π/6 = 7π/6 rads
π + π/4 = 5π/4 rads
π + π/3 = 4π/3 rads
Quadrant 4
360° − 30° = 330°
360° − 45° = 315°
360° − 60° = 300°
2π − π/6 = 11π/6 rads
2π − π/4 = 7π/4 rads
2π − π/3 = 5π/3 rads
Examples
Conversions
