# 2cscx

Input |
---|

2 csc(x) |

Alternate form assuming x is real |

-(4 sin(x))/(cos(2 x) – 1) |

Roots |

(no roots exist) |

Series expansion at x=0 |

2/x + x/3 + (7 x^3)/180 + (31 x^5)/7560 + O(x^6) (Laurent series) |

Derivative |

d/dx(2 csc(x)) = -2 cot(x) csc(x) |

Indefinite integral |

integral 2 csc(x) dx = 2 log(sin(x/2)) – 2 log(cos(x/2)) + constant |

Local maxima |

max{2 csc(x)} = -2 at x = 2 pi n – pi/2 for integer n |

Local minima |

min{2 csc(x)} = 2 at x = 2 pi n + pi/2 for integer n |