# 1 sinx

Input |
---|

1 sin(x) |

Result |

sin(x) |

Alternate form |

1/2 i e^(-i x) – 1/2 i e^(i x) |

Roots |

x = pi n, n element Z |

Series expansion at x=0 |

x – x^3/6 + x^5/120 + O(x^6) (Taylor series) |

Derivative |

d/dx(1 sin(x)) = cos(x) |

Indefinite integral |

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

Global maxima |

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

Definite integral over a half-period |

integral_0^pi sin(x) dx = 2 |

Definite integral mean square |

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