# How to use the COT function

**What is the COT function?**

The COT function calculates the cotangent of an angle specified in radians.

**What is the cotangent?**

The cotangent is one of the trigonometric functions closely related to the tangent function.

The cot function is defined as the ratio between the the length of adjacent side and length of the opposite side of a right triangle.

cot(Î¸) = adjacent / opposite

or

defined as the reciprocal of tangent:

cot(Î¸) = 1 / tan(Î¸)

The cotangent equals the ratio of the cos and sin:

cot(Î¸) = cos(Î¸) / sin(Î¸)

**What is the angle Î¸?**

The Greek letter theta (Î¸) is commonly used to represent an unknown angle in a right triangle.

**What is a right triangle?**

A right triangle is a type of triangle that contains one internal angle measuring 90 degrees or Ï€/2 radians (a right angle).

**What are radians?**

Radians are a unit used to measure angles. An angle of 1 radian has an arc length equal to the circle's radius.

**What is the relationship between the number pi and radians?**

Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2Ï€ multiplied by the circle's radius (2Ï€r).

Since the circumference goes all the way around a circle, that means the full circle measures 2Ï€ radians. Half a circle would be Ï€ radians (half of 2Ï€). A quarter circle is 2Ï€/4 = Ï€/2 radians. An eighth of a circle is 2Ï€/8 = Ï€/4 radians.

Excel has a function that returns the number pi:Â PI function

**What are the main trigonometric functions, their domain and range?**

Function |
Domain (input) |
Range (output) |

sin(x) | All real numbers | (-1, 1) |

cos(x) | All real numbers | (-1, 1) |

tan(x) | All real numbers except multiples of Ï€/2 | (-âˆž, âˆž) |

sec(x) | All real numbers except multiples of Ï€ | (1, âˆž) U (-âˆž, -1) |

csc(x) | All real numbers except integer multiples of Ï€ | (-âˆž, -1) U (1, âˆž) |

cot(x) | All real numbers except integer multiples of Ï€ | (-âˆž, âˆž) |

**What are the main trigonometric arcfunctions, their domain and range?**

Function |
Domain (input) |
Range (output) |

sin^{-1}(x) |
[-1, 1] | (-Ï€/2, Ï€/2) |

cos^{-1}(x) |
[-1, 1] | (0, Ï€) |

tan^{-1}(x) |
All real numbers | (-Ï€/2, Ï€/2) |

sec^{-1}(x) |
[-1, 1] | (0, Ï€/2) U (Ï€/2, Ï€) |

csc^{-1}(x) |
[-1, 1] | (-Ï€/2, -0) U (0, Ï€/2) |

cot^{-1}(x) |
All real numbers | (0, Ï€) |

**What is the trigonometric domain?**

The domain of a trigonometric function refers to the set of input values it is defined and valid for. The secant, cosecant, and cotangent functions have restricted domains due to their asymptotes.

**What is the trigonometric range?**

The range of a trigonometric function refers to the set of possible output values it returns.

**What are asymptotes in terms of the cotangent function?**

Asymptotes are vertical lines that the function approaches but never reaches. Cotangent has vertical asymptotes at integer multiples of Ï€.

## 1. COT Function Syntax

COT(*number*)

## 2. COT Function Arguments

number |
Â Required. An angle in radians. |

### Comments

Use the RADIANS function to convert degrees to radians.

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What is the RADIANS function? The RADIANS function converts degrees to radians. What is radian? Radians measure angles by the […]

## 3. COT Function examples

Formula in cell C3:

### Functions in 'Math and trigonometry' category

The COT function function is one of 73 functions in the 'Math and trigonometry' category.

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