# 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 $\frac{3\pi}{5}$.

Title | radian |
---|---|

Canonical name | Radian |

Date of creation | 2013-03-22 14:48:58 |

Last modified on | 2013-03-22 14:48:58 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 7 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 51M04 |

Synonym | absolute unit of angle |

Related topic | SolidAngle |