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# preap precalculus

### trig identities

Question | Answer |
---|---|

sinx | 1/cscx |

cosx | 1/secx |

sin^2x + cos^2x | 1 |

tan^2x + 1 | sec^2x |

1 + cot^2x | csc^2x |

sin(-x) | -sinx [odd] |

csc(-x) | -cscx [odd] |

cos(-x) | cosx [even] |

sec(-x) | secx [even] |

tan(-x) | -tanx [odd] |

cot(-x) | -cotx [odd] |

sinx (cofunction) | cos(pi/2 - x) |

tanx (cofunction) | cot(pi/2 - x) |

secx (cofunction) | csc(pi/2 - x) |

sin(x+y) | sinxcosy + cosxsiny |

sin(x-y) | sinxcosy - cosxsiny |

cos(x+y) | cosxcosy - sinxsiny |

cos(x-y) | cosxcosy + sinxsiny |

tan(x+y) | (tanx + tany)/(1 - tanxtany) OR sin(x+y)/cos(x+y) |

tan(x-y) | (tanx - tany)/(1 + tanxtany) OR sin(x-y)/cos(x-y) |

sin2x | 2sinxcosx |

cos2x | cos^2x - sin^2x OR 2cos^x - 1 OR 1 - 2sin^2x |

tan2x | 2tanx/(1 - tan^2x) OR sin2x/cos2x |

sin(x/2) | +-sqrt (1-cosx)/2 |

cos(x/2) | +-sqrt (1+cosx)/2 |

tan(x/2) | (1-cosx)/sinx OR sinx/(1+cosx) |

sin^2a | (1-cos2a)/2 |

cos^2a | (1+cos2a)/2 |

tan^2a | sin^2a/cos^2a OR (1-cos2a)/(1+cos2a) |

Created by:
qiguai