# Trigonometry Formulas | Sign of Trigonometric Functions in Different Quadrants

The branch of mathematics that focuses on relationships between the sides and angles of triangles is called trigonometry. The word trigonometry comes from the Latin derivative of Greek words for the triangle (trigonon) and measure (metron).

As we know without a formula no operation can be performed. Here are important formulas that help the student to solve difficult problems

## Reciprocal Identities

## Even and odd Formulas

sin(−θ) = −sin θ

cos(−θ) = cos θ

tan(−θ) = −tan θ

cosec(−θ) = −cosecθ

sec(−θ) = sec θ

cot(−θ) = −cot θ

## Pythagorean Identities

Sin^{2} θ = 1- Cos^{2} θ

Sin^{2} θ + Cos^{2} θ = 1

Sec^{2} θ = 1 + Tan^{2} θ

Cosec^{2} θ = 1+ Cot^{2} θ

sin(π/2-A) = cos A

cos(π/2-A) = sin A

sin(π-A) = sin A

cos(π-A) = -cos A

sin(π+A)=-sin A

cos(π+A)=-cos A

sin(2π-A) = -sin A

cos(2π-A) = cos A

## 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

## Sign of Trigonometric Functions in Different Quadrants

Quadrant | I | II | III | IV |

Sin θ | + | + | – | – |

coos θ | + | – | – | + |

tan θ | + | – | + | – |

sec θ | + | + | – | – |

cosec θ | + | – | – | + |

cot θ | + | – | + | – |

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