Online arctan(x) calculator. Inverse tangent calculator.

## Arctangent definition

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°

## Graph of arctan

## Arctan rules

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

Tangent of arctangent | tan( arctan |

Arctan of negative argument | arctan(- |

Arctan sum | arctan |

Arctan difference | arctan |

Sine of arctangent | |

Cosine of arctangent | |

Reciprocal argument | |

Arctan from arcsin | |

Derivative of arctan | |

Indefinite integral of arctan |

## Arctan table

x | arctan(x) (rad) | arctan(x) (°) |
---|---|---|

-∞ | -π/2 | -90° |

-3 | -1.2490 | -71.565° |

-2 | -1.1071 | -63.435° |

-√3 | -π/3 | -60° |

-1 | -π/4 | -45° |

-1/√3 | -π/6 | -30° |

-0.5 | -0.4636 | -26.565° |

0 | 0 | 0° |

0.5 | 0.4636 | 26.565° |

1/√3 | π/6 | 30° |

1 | π/4 | 45° |

√3 | π/3 | 60° |

2 | 1.1071 | 63.435° |

3 | 1.2490 | 71.565° |

∞ | π/2 | 90° |

## Arctan on calculator

In order to calculate arctan(y) on a calculator:

- Press shift+tan buttons.
- Enter the angle.
- Press the
*Calculate*button.

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