# Cos4x

Input |
---|

cos(4 x) |

Roots |

x = (pi n)/4 – pi/8, n element Z |

Series expansion at x=0 |

1 – 8 x^2 + (32 x^4)/3 + O(x^6) (Taylor series) |

Derivative |

d/dx(cos(4 x)) = -4 sin(4 x) |

Indefinite integral |

integral cos(4 x) dx = 1/4 sin(4 x) + constant |

Global maxima |

max{cos(4 x)} = 1 at x = (pi n)/2 for integer n |

Definite integral |

integral_0^(pi/8) cos(4 x) dx = 1/4 = 0.25 |

Definite integral mean square |

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