UNITS OF MEASUREMENTS OF ANGLES

UNITS OF MEASUREMENTS OF ANGLES
Radian : The angle subtended from the centre of a circle which intercepts an arc equal in length to the radius of the circle.
    It is represented by rad or ^c.
Ex : 1.5 radians is written as 1.5 rad or 1.5^c
The angle subtended by an arc in radians of a circle is defined as the ratio of the arc length to the radius of the circle.
    \(\theta = \frac{{{\text{arc length}}}}{{{\text{radius}}}} = \frac{l}{r}\)
    Therefore arc length \(l=r\theta\)
If we consider the arc to be the total circumference of the circle, then arc length = \(2\pi r\) . Also, we know that the angle subtended at the center of the circle by its circumference is \(360^0\) . Then by the above formula,
    Angle subtended = (arc length)/(radius)
Then,
       \(\theta\) = arc length/radius = s/r radians
Note:

ii) If the measure of an angle in degree and radian be D, G and C respectively, then
\(\frac{D}{{180}} = \frac{G}{{200}} = \frac{C}{\pi }\)