# 1/secx

Input |
---|

1/(sec(x)) |

Result |

cos(x) |

Alternate form |

e^(-i x)/2 + e^(i x)/2 |

Roots |

x = pi n – pi/2, n element Z |

Series expansion at x=0 |

1 – x^2/2 + x^4/24 + O(x^6) (Taylor series) |

Derivative |

d/dx(1/(sec(x))) = -sin(x) |

Indefinite integral |

integral cos(x) dx = sin(x) + constant |

Global maxima |

max{1/(sec(x))} = 1 at x = 2 pi n for integer n |

Definite integral |

integral_0^(pi/2) cos(x) dx = 1 |

Definite integral mean square |

integral_0^(2 pi) (cos^2(x))/(2 pi) dx = 1/2 = 0.5 |