**Trigonometry Function Formulas**

**Trigonometry Function Formulas of a Right Triangle :**

sin α = a / c = opposite / hypotenuse

cos α = b / c = adjacent / hypotenuse

tan α = a / b = opposite / adjacent

cot α = b / a = adjacent / opposite

sec α = c / b Cosec α = c / a

**Basic Formula :**

sin^{2} α + cos^{2} α = 1

tan α . cot tan α = 1

tan α = sin α / cos α = 1 / cot tan α

cot tan α = cos α / sin α = 1 / tan α

1 + tan^{2} α = 1 / cos^{2} α = sec^{2} α

1 + cot tan^{2} α = 1 / sin^{2} α = cos sec^{2} α

**Trigonometr**ic Table

α | 0^{0} | 30^{0} | 45^{0} | 60^{0} | 90^{0} | 120^{0} | 180^{0} | 270^{0} | 360^{0} |

sin α | 0 | 1/2 | √2/2 | √3/2 | 1 | √3/2 | 0 | -1 | 0 |

cos α | 1 | √3/2 | √2/2 | 1/2 | 0 | -1/2 | -1 | 0 | 1 |

tan α | 0 | 1/√3 | 1 | √3 | ∞ | -√3 | 0 | ∞ | 0 |

cot α | ∞ | √3 | 1 | 1/√3 | 0 | -1/√3 | ∞ | 0 | ∞ |

sec α | 1 | 2/√3 | √2 | 2 | ∞ | -2 | -1 | ∞ | 1 |

cosec α | ∞ | 2 | √2 | 2/√3 | 1 | 2/√3 | ∞ | -1 | ∞ |

**Co-Ratios**

sin | cos | tan | cot | |

-α | -sin α | +cos α | -tan α | -cot α |

90^{0} – α | +cos α | +sin α | +cot α | +tan α |

90^{0} + α | +cos α | -sin α | -cot α | -tan α |

180^{0} – α | +sin α | -cos α | -tan α | -cot α |

180^{0} + α | -sin α | -cos α | +tan α | +cot α |

270^{0} – α | -cos α | -sin α | +cot α | +tan α |

270^{0} + α | -cos α | +sin α | -cot α | -tan α |

360^{0}k – α | -sin α | +cos α | -tan α | -cot α |

360^{0}k – α | +sin α | +cos α | +tan α | +cot α |

**Trigonometry Addition Formula:**

- sin(A + B) = sinA cosB + cosA sinB
- sin(A – B) = sinA cosB – cosA sinB

- cos(A + B) = cosA cosB – sinA sinB
- cos(A – B) = cosA cosB + sinA sinB

- tan (A + B) = tanA + tanB / 1 – tanA tanB
- tan(A – B) = tanA – tanB / 1 + tanA tanB

- cot (A+ B) = cotA cotB – 1 / cotA + cotB

**Product of Trigonometric Functions:**

- sin α cos β = 1/2 [ sin (α + β) + sin(α – β)]
- cos α cos β = 1/2 [ sin (α + β) + sin(α – β)]
- cos α cos β = 1/2 [ cos (α + β) + cos(α – β)]
- sin α sin β = 1/2 [ cos (α – β) + cos(α + β)]

- tan α tan β = tan α + tan β / cot tan α + cot tanβ = – tanα – tan β / cot tan α – cot tan β

Trigonometric Formula with t = tan(x/2)

sinx = 2t / 1 + t^{2}

cos x = 1 – t^{2} / 1 + t^{2}

tan x = 2t / 1 – t^{2}

cot x = 1 – t^{2} / 2t

**Trigonometric Relation Between Functions:**

**Angle of a Plane Triangle :**

- A, B, C are 3 angles of a triangle
- sin A + sin B + sin c = 4 cos(A / 2) cos(B/2) cos(C/2)
- cosA + cos B + cos C = 4 sin(A/2) sin(B/2) sin(C/2) + 1
- sinA + sinB – sinC = 4sin (A/2) sin (B/2) cos (C/2)

Please visit this page to get more updates on Math Shortcut Tricks and Trigonometry Function Formulas. You can also like our facebook page to get updates.

If you have any question regarding **Trigonometry Function Formulas** then please do comment on below section. You can also send us message on facebook.

This is good?????

Intellegent

Sir me mathematics ka silvers chAiye

Please let these formulaes in easy way ..

And don’t expand it so much..

if n is a natural number .which is the solution to the equation tan(5a)=cot(3a)?

a=alpha symbol

Nice formulaes