# 1-2cosx

Input |
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1 – 2 cos(x) |

Alternate form |

-e^(-i x) – e^(i x) + 1 |

Series expansion at x=0 |

-1 + x^2 – x^4/12 + O(x^6) (Taylor series) |

Derivative |

d/dx(1 – 2 cos(x)) = 2 sin(x) |

Indefinite integral |

integral (1 – 2 cos(x)) dx = x – 2 sin(x) + constant |

Global minima |

min{1 – 2 cos(x)} = -1 at x = 2 pi n for integer n |

Definite integral over a half-period |

integral_0^pi (1 – 2 cos(x)) dx = pi~~3.14159 |

Definite integral over a period |

integral_0^(2 pi) (1 – 2 cos(x)) dx = 2 pi~~6.28319 |

Definite integral mean square |

integral_0^(2 pi) (1 – 2 cos(x))^2/(2 pi) dx = 3 |