Тригонометрия (Шпаргалка)

sin^2(a)+cos^2(a)=1;                     |Sin Cos Tg

tg(a)=sin(a)/cos(a);                     |++  -+  -+

tg(a)ctg(a)=1;                           |--  -+  +-

1+tg^2(a)=1/cos^2(a);                    |

1+ctg^2(a)=1/sin^2(a);                   |sin(p/2+-a)=cos(a);

                                         |sin(p+-a)=-+sin(a);

sin(a+b)=sin(a)cos(b)+cos(a)sin(b);      |sin(3p/2+-a)=-cos(a);

sin(a-b)=sin(a)cos(b)-cos(a)sin(b);      |sin(2p+-a)=+-sin(a);

cos(a+b)=cos(a)cos(b)-sin(a)sin(b);      |

cos(a-b)=cos(a)cos(b)+sin(a)sin(b);      |cos(p/2+-a)=+-sin(a);

tg(a+b)=tg(a)+tg(b)/1-tg(a)tg(b);        |cos(p+-a)=-cos(a);

tg(a-b)=tg(a)-tg(b)/1-tg(a)tg(b);        |cos(3p/2+-a)=+-sin(a);

ctg(a+b)=ctg(a)ctg(b)-1/ctg(a)+ctg(b);   |cos(2p+-a)=cos(a);

ctg(a-b)=ctg(a)ctg(b)+1/ctg(b)-ctg(a);   |

                                         |tg(p/2+-a)=-+ctg(a)

sin(2a)=2sin(a)cos(a);                   |tg(p+-a)=+-tg(a)

cos(2a)=cos^2(a)-sin^2(b)=1-2sin^2(a);   |tg(3p/2+-a)=-+ctg(a)

tg(2a)=2tg(a)/1-tg^2(a);                 |tg(2p+-a)=+-tg(a)

ctg(2a)=ctg^2(a)-1/2ctg(a);              |

sin(3a)=3sin(a)-4sin^3(a);               |ctg(p/2+-a)=-+tg(a)

tg(3a)=3tg(a)-tg^3(a)/1-3tg^2(a);        |ctg(p+-a)=+-ctg(a)

ctg(3a)=3ctg(a)-ctg^3(a)/1-3ctg^2(a);    |ctg(3p/2+-a)=-+tg(a)

                                         |ctg(2p+-a)=+-ctg(a)

sin^2(a/2)=1-cos(a)/2;                   |

cos^2(a/2)=1+cos(a)/2;                   |

tg^2(a/2)=1-cos(a)/1+cos(a);             |

ctg^2(a/2)=1+cos(a)/1-cos(a);            |

tg(a/2)=sin(a)/1+cos(a)=1-cos(a)/sin(a); |

ctg(a/2)=sin(a)/1-cos(a)=1+cos(a)/sin(a);|

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sin(a)+sin(b)=2sin(a+b/2)cos(a-b/2);     |

sin(a)-sin(b)=2sin(a-b/2)cos(a+b/2);     |

cos(a)+cos(b)=2cos(a+b/2)cos(a-b/2);     |

cos(a)-cos(b)=-2cos(a+b/2)cos(a-b/2)=    |

=2cos(a+b/2)cos(b-a/2);                  |

cos(a)+sin(b)=sqrt(2)cos(45-a);          |

cos(a)-sin(b)=sqrt(2)sin(45-a);          |

tg(a)+tg(b)=sin(a+b)/cos(a)cos(b);       |

tg(a)-tg(b)=sin(a-b)/cos(a)cos(b);       |

ctg(a)+ctg(b)=sin(a+b)/sin(a)sin(b);     |

ctg(a)-ctg(b)=sin(b-a)/sin(a)sin(b);     |

tg(a)+ctg(b)=cos(a-b)/cos(a)sin(b);      |

tg(a)-ctg(b)=-cos(a+b)/cos(a)sin(b);     |

tg(a)+ctg(a)=2/sin(2a);                  |

tg(a)-ctg(a)=-2ctg(2a);                  |

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sin(a)sin(b)=1/2(cos(a-b)-cos(a+b));     |

cos(a)cos(b)=1/2(cos(a+b)+cos(a-b));     |

sin(a)cos(b)=1/2(sin(a+b)+sin(a-b));     |

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sin(a)=2tg(a/2)/1+tg^2(a/2);             |

cos(a)=1-tg^2(a/2)/1+tg^2(a/2);          |

tg(a)=2tg(a/2)/1-tg^2(a/2);              |

ctg(a)=1-tg^2(a/2)/2tg(a/2);             |