# Cotangent Calculator

Use this calculator to easily calculate the cotangent of an angle given in degrees or radians.

## Cotangent function ( cot(x) or cotan(x) )

The tangent is a trigonometric function, defined as the ratio of the length of the side adjacent to the angle to the length of the opposite side, in a right-angled triangle. It is called "cotangent" in reference to the tangent function, which can be represented as a line segment tangent to a circle.

A cotangent of an angle α is also equal to the ratio between its cosine and sine, so cotα = cosα / sinα. Following from the definition, the function results in an undefined value at certain angles, like 0°, 180°, 360°, and so on.

## Related trigonometric functions

The **reciprocal of cotangent** is the tangent: tan(x), which is the ratio of the length of the opposite side to the length of the side adjacent to the angle.

The **inverse of the cotangent** is the arccotangent function: arccot(x).

## How to calculate the cotangent of an angle?

Our cotangent calculator accepts input in degrees or radians, so once you have your angle measurement, just type it in and press "calculate". This is how easy it is.

## Applications of the cotangent function

The cotangent function is used in the ASA triangle rule (angle-side-angle). Other than that, it has not had many practical applications since calculators became common, so you should rarely come across it.

Above: the cot calculator output for increasing angle values in degrees.

Table of common cotangent values:

x (°) | x (rad.) | cot(x) |
---|---|---|

0° | 0 | undefined |

30° | π/6 | 1.732051 |

45° | π/4 | 1 |

60° | π/3 | 0.577350 |

90° | π/2 | 0 |

120° | 2π/3 | -0.577350 |

135° | 3π/4 | -1 |

150° | 5π/6 | -1.732051 |

180° | π | undefined |

#### Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:

Georgiev G.Z., *"Cotangent Calculator"*, [online] Available at: https://www.gigacalculator.com/calculators/cot-calculator.php URL [Accessed Date: 23 Jul, 2019].