radian

The radian is a of angle used in the higher mathematics.  The magnitude of an angle $\alpha$ is one radian, if the arc corresponding the angle $\alpha$ as a central angle of a circle is equally long as the radius of the circle.  Thus, a radian is equal to $\frac{180}{\pi }$ , minutes and seconds approximately ${57}^{\mathrm{o}}{\mathrm{\hspace{0.17em}17}}^{\prime }{\mathrm{\hspace{0.17em}44.80625}}^{\prime \prime }.$

In degrees, a circle has 360 degrees, while in radians a circle has $2\pi$ radians. In fact, many angles of equilateral polygons are equal to a multiple of $\pi$ divided by some integer: for example, the interior angle of an equilateral triangle’s vertex is $\frac{\pi }{3}$, while the interior angle of an equilateral pentagon’s vertex is $\frac{3\pi }{5}$.