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

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 $$S = r\theta $$.