# Cos2x 1

Input |
---|

cos(2 x)×1 |

Result |

cos(2 x) |

Roots |

x = (pi n)/2 – pi/4, n element Z |

Series expansion at x=0 |

1 – 2 x^2 + (2 x^4)/3 + O(x^6) (Taylor series) |

Derivative |

d/dx(cos(2 x)×1) = -2 sin(2 x) |

Indefinite integral |

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

Global maxima |

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

Definite integral |

integral_0^(pi/4) cos(2 x) dx = 1/2 = 0.5 |

Definite integral mean square |

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