Online trigonometric tangent calculator.

## Tangent calculator

* Use e for scientific notation. E.g: 5e3, 4e-8, 1.45e12

## Inverse tangent calculator

## Tangent definition

In a right triangle ABC the tangent of α, tan(α) is defined as the ratio between the side opposite to angle α and the side adjacent to the angle α:

tan *α* = *a* / *b*

#### Example

*a* = 3"

*b* = 4"

tan *α* = *a* / *b* = 3 / 4 = 0.75

## Graph of tangent

## Tangent rules

Rule name | Rule |
---|---|

Symmetry | tan(- |

Symmetry | tan(90°- θ) = cot θ |

tan θ = sin θ / cos θ | |

tan θ = 1 / cot θ | |

Double angle | tan 2θ = 2 tan θ / (1 - tan^{2} θ) |

Angles sum | tan(α+β) = (tan α + tan β) / (1 - tan α tan β) |

Angles difference | tan(α-β) = (tan α - tan β) / (1 + tan α tan β) |

Derivative | tan' x = 1 / cos^{2}(x) |

Integral | ∫ tan x dx = - ln |cos x| + C |

Euler's formula | tan x = (e - ^{ix}e^{-ix}) / i (e + ^{ix}e^{-ix}) |

## Inverse tangent function

The arctangent of x is defined as the inverse tangent function of x when x is real (x∈ℝ).

When the tangent of y is equal to x:

tan *y* = *x*

Then the arctangent of x is equal to the inverse tangent function of x, which is equal to y:

arctan *x *= tan^{-1}* x* = *y*

#### Example

arctan 1 = tan^{-1} 1 = π/4 rad = 45°

See: Arctan function

## Tangent table

x (rad) | x (°) | tan(x) |
---|---|---|

-π/2 | -90° | -∞ |

-1.2490 | -71.565° | -3 |

-1.1071 | -63.435° | -2 |

-π/3 | -60° | -√3 |

-π/4 | -45° | -1 |

-π/6 | -30° | -1/√3 |

-0.4636 | -26.565° | -0.5 |

0 | 0° | 0 |

0.4636 | 26.565° | 0.5 |

π/6 | 30° | 1/√3 |

π/4 | 45° | 1 |

π/3 | 60° | √3 |

1.1071 | 63.435° | 2 |

1.2490 | 71.565° | 3 |

π/2 | 90° | ∞ |

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