Results of Angles with Degree and Radian

1) ANGLE: The union of two non collinear rays which has common end point is called an angle.

2) RADIAN: Angle subtended at the centre of a circle by an arc of length equal to the radius of the circle is called angle of one radian.

3) A circle contains  = 2\pi Radians

4) A circle contains  = {180^  \circ } Degrees

5) \pi Radians  = 180 Degrees

6) 1 Degree  = 60 Minutes = 60'

7) 1 Minute  = 60 Second  = 60''

8) 1 Radian  = \frac{{{{180}^ \circ }}}{\pi } = {57.295778^  \circ } = {57^ \circ }17'44.8''

9) {1^ \circ } = \frac{\pi  }{{180}} = 0.01745 Radian

10)

Degrees

{30^ \circ }

{45^ \circ }

{60^ \circ }

{90^ \circ }

{120^ \circ }

{135^ \circ }

{150^ \circ }

{180^ \circ }

Radians

\frac{\pi }{6}

\frac{\pi }{4}

\frac{\pi }{3}

\frac{\pi }{2}

\frac{{2\pi }}{3}

\frac{{3\pi }}{4}

\frac{{5\pi }}{6}

\pi

 

11) If \theta is the angle (measured in radians) subtended at the centre of a circle of radius r by an arc of length S, then S  = r\theta .