# Cos2x 1 2

Input |
---|

cos(2 x)×1×2 |

Result |

2 cos(2 x) |

Roots |

x = (pi n)/2 – pi/4, n element Z |

Series expansion at x=0 |

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

Derivative |

d/dx(cos(2 x)×2) = -4 sin(2 x) |

Indefinite integral |

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

Global maxima |

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

Definite integral |

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

Definite integral mean square |

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