# 2cosx-1

Input |
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2 cos(x) – 1 |

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(2 cos(x) – 1) = -2 sin(x) |

Indefinite integral |

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

Global maxima |

max{2 cos(x) – 1} = 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 |