# 1 2cos x

Input |
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2 cos(x) |

Alternate form |

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

Roots |

x = pi n – pi/2, n element Z |

Series expansion at x=0 |

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

Derivative |

d/dx(2 cos(x)) = -2 sin(x) |

Indefinite integral |

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

Global maxima |

max{2 cos(x)} = 2 at x = 2 pi n for integer n |

Definite integral |

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

Definite integral mean square |

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