If a rotation from the initial side to terminal side is $\left( \dfrac{1}{360} \right)^{\text {th}}$ of a revolution, the angle is said to have a measure of one degree, written as $1^o$ .

A degree is divided in 60 minutes and a minute is divided in 60 seconds

$1^o=60',\quad 1'=60"$

Some angles are shown below (In degree)

Radian Measure

Angle subtended at the centre by an arc of length $1 \text{ unit}$ in a unit cirlce (circle of radius $1 \text{ unit}$ is said to be a measure of $1$ radian.

The circumference of a circle of radius $1 \text{ unit} \text{ is } 2\pi$ . Thus, one complete revolution of the initial sides subtends an angle of $2\pi$ radian.

In a circle of radius $r$ , an arc of length or subtends an angle whose measure is $1$ radian, an arc of length $l$ will subtend an angle whose measure is $\dfrac{l}{r}\text{ radian}$ .

Thus, is a circle of radius $r$ , an arc length length $l$ subtends an angle $\theta$ radian at centre, we have

$\theta =\dfrac{l}{r}\text{ or } l=r\theta$

Some angles whose measures are in radian shown below:

Relation Between Degree and Radians

$2\pi \text { radian }= 360^o$

Or $\pi\text { radian}= 180^o \left( \therefore \pi=\dfrac{22}{7}\text { or } 3.1415\right)$

$\implies 1 \text { radian}= \dfrac{180^o}{\pi}=57^o16'(\text{ approx.)}$

Also, $1^o=\dfrac{\pi }{180}\text { radian }= 0.01746 \text{ radian} (\text{ approx.)}$

Degree	$30^o$	$45^o$	$60^o$	$90^o$	$180^o$	$270^o$	$360^o$
Radian	$\dfrac {\pi}{6}$	$\dfrac {\pi}{4}$	$\dfrac {\pi}{3}$	$\dfrac {\pi}{2}$	$\pi$	$\dfrac {3\pi}{2}$	$2 \pi$