Results of Angles with Degree and Radian

1) ANGLE: The union of two non colinear rays which have a common end point is called an angle.
2) RADIAN: An angle subtended at the center of a circle by an arc of length equal to the radius of the circle is called the 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 seconds  = 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 center of a circle of radius r by an arc of length S, then S = r\theta .