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# Trig Identities

Term | Definition |
---|---|

reciprocal identities | secθ = 1/cosθ<br /> cscθ = 1/sinθ<br /> cotθ = 1/tanθ |

quotient identities | tanθ = sinθ/cosθ<br /> cotθ = cosθ/sinθ |

odd-even identities | -sinθ = sin(-θ)<br /> cosθ = cos(-θ)<br /> -tanθ = tan(-θ)<br /> -cscθ = csc(-θ)<br /> secθ = sec(-θ)<br /> -cotθ = cot(-θ) |

cofunction identities | sinθ = cos(π/2 - θ)<br /> cosθ = sin(π/2 - θ)<br /> tanθ = cot(π/2 - θ)<br /> cscθ = sec(π/2 - θ)<br /> secθ = csc(π/2 - θ)<br /> cotθ = tan(π/2 - θ) |

pythagorean identities | sin^2θ + cos^2θ = 1<br /> 1 + tan^2θ = sec^2θ<br /> 1 + cot^2θ = csc^2θ |

sum and difference identities | sin(α + β) = sinαcosβ + cosαsinβ<br /> sin(α - β) = sinαcosβ - cosαsinβ<br /> cos(α + β) = cosαcosβ - sinαsinβ<br /> cos(α - β) = cosαcosβ + sinαsinβ<br /> tan(α + β) = (tanα + tanβ)/(1 - tanαtanβ)<br /> tan(α - β) = (tanα - tanβ)/(1 + tanαtanβ) |

double-angle identities | sin2θ = 2sinθcosθ<br /> cos2θ = cos^2θ - sin^2θ,<br /> 2cos^2θ - 1,<br /> 1 - 2sin^2θ<br /> tan2θ = (2tanθ)/(1 - tan^2θ) |

half-angle identities | sin(1/2)θ = +/- √(1 - cosθ)/(2)<br /> cos(1/2)θ = +/- √(1 + cosθ)/(2)<br /> tan(1/2)θ = +/- √(1 - cosθ)/(1 + cosθ) |

product-to-sum identities | sinαsinβ = (1/2)[cos(α - β) - cos(α + β)]<br /> cosαcosβ = (1/2)[cos(α - β) + cos(α + β)]<br /> sinαcosβ = (1/2)[sin(α + β) + sin(α - β)] |

Created by:
carrielynn28