Radian is an alternative use for the measurement of angle. Abbreviation for radian is rad. $1$ rad

Question

Radian is an alternative use for the measurement of angle.
Abbreviation for radian is rad.
$1$ radian is the measure of an angle subtended at the centre of a circle by an arc equal in length to the radius.
So $2\pi$ radians $=360{}^\circ$
Conversions between radians and degrees.

Arc Length

Angle in degrees

Angle in radians

Length of the minor arc $PXQ$

$= \frac{x^\circ}{360^\circ} \times \text{circumference}$

$= \frac{x^\circ}{360^\circ} \times 2\pi r$

where $x^\circ$ is the angle subtended by the arc at the centre of the circle of radius $r$.

Length of the minor arc $AXB$

$= \frac{\theta}{2\pi} \times \text{circumference} \quad (360{}^\circ = 2\pi \text{ radian})$

$= \frac{\theta}{2\pi} \times 2\pi r$

$= r\theta$

where $\theta$ radians is the angle subtended by the arc at the centre of the circle of radius $r$.

Area of Sector

Angle in degrees

Angle in radians

Area of the minor sector $OPXQ$

$= \frac{x{}^\circ}{360{}^\circ} \times \text{area of circle}$

$= \frac{x{}^\circ}{360{}^\circ} \times \pi r^2$

where $x{}^\circ$ is the angle subtended by the arc at the centre of the circle of radius $r$.

Area of the minor sector $OAXB$

$= \frac{\theta}{2\pi} \times \text{area of circle} \quad (360{}^\circ = 2\pi \text{ radian})$

$= \frac{\theta}{2\pi} \times \pi r^2$

$= \frac{1}{2} r^2\theta$

where $\theta$ radians is the angle subtended by the arc at the centre of the circle of radius $r$.

Accepted Answer

$\pi\text{ rad}=180^\circ$, $\ell=r\theta$, $A=\dfrac12r^2\theta$ for $\theta$ in radians

Radian Measure