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Trigonometric Identities

This page is meant to serve as a quick overview of the trigonometric identities.

**Reciprocal Identities**

cot Θ = 1 / tan Θ |
sec Θ = 1 / cos Θ |
csc Θ = 1 / sin Θ |

tan Θ = 1 / cot Θ |
cos Θ = 1 / sec Θ |
sin Θ = 1 / csc Θ |

**Quotient Identities**

tan Θ = sin Θ / cos Θ |
cot Θ = cos Θ / sin Θ |

**Pythagorean Identities**

sin² Θ + cos² Θ = 1 |
tan² Θ + 1 = sec² Θ |
1 + cot² Θ = csc² Θ |

**Negative-Angle Identities**

sin (-Θ) = -sin Θ |
cos (-Θ) = -cos Θ |
tan (-Θ) = -tan Θ |

**Cofunction Identities**

For any acute angle Θ in standard position, the following applies:

sin Θ = cos(90-Θ) | cos Θ = sin(90-Θ) | tan Θ = cot(90-Θ) |

csc Θ = sec(90-Θ) | sec Θ = csc(90-Θ) | cot Θ = tan(90-Θ) |

**Sum and Difference Identities**

cos (A - B) = cos A cos B + sin A sin B | cos (A + B) = cos A cos B - sin A sin B |

sin (A + B) = sin A cos B + cos A sin B | sin (A - B) = sin A cos B - cos A sin B |

**Double-Angle Identities**

**Half-Angle Identities**