# Cosx 3

Input |
---|

cos(x)×3 |

Result |

3 cos(x) |

Alternate form |

(3 e^(-i x))/2 + (3 e^(i x))/2 |

Roots |

x = pi n – pi/2, n element Z |

Series expansion at x=0 |

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

Derivative |

d/dx(cos(x)×3) = -3 sin(x) |

Indefinite integral |

integral 3 cos(x) dx = 3 sin(x) + constant |

Global maxima |

max{cos(x) 3} = 3 at x = 2 pi n for integer n |

Definite integral |

integral_0^(pi/2) 3 cos(x) dx = 3 |

Definite integral mean square |

integral_0^(2 pi) (9 cos^2(x))/(2 pi) dx = 9/2 = 4.5 |