Every function has an inverse in the trigonometry. This operation inverses the function, so the cotangent becomes inverse cotangent through this method. Then, the inverse cotangent is used to evaluate the degree value of the angle in the triangle(right-angled) when the sides opposite to and adjacent to the angles are known.

So each trigonometric function has an inverse. Below are the six trigonometric functions.

- Sine
- Cosine
- Tangent
- Secant
- Cosecant
- Cotangent

The inverse of these trigonometric functions are as follows:

- inverse sine (or) arcsine
- inverse cosine (or) arccos
- inverse tangent (or) arctan
- inverse secant (or) arcsec
- inverse cosecant (or) arccsc
- inverse cotangent (or) arccot

The inverse of Cotangent is also denoted as arccot or Cot^{-1}.

## The Formula for arccot is:

Cotangent = Base / Perpendicular |

If in a triangle, the base of the angle A is 1 and the perpendicular side is âˆš3.

So, cot^{-1 }(1/âˆš3) = A

cot A = 1/âˆš3

cot A = cot 60Â°

A = 60Â°

## Table values of arccot

The below table shows the values of arccot.

x | arccot(x) | arccot(x) |

-âˆš3 | 5Ï€/6 | 150Â° |

-1 | 3Ï€/4 | 135Â° |

-âˆš3/3 | 2Ï€/3 | 120Â° |

0 | Ï€/2 | 90Â° |

âˆš3/3 | Ï€/3 | 60Â° |

1 | Ï€/4 | 45Â° |

âˆš3 | Ï€/6 | 30Â° |

## Solved Examples

**Example 1: If x = cot ^{-1}(-âˆš3/3), then what is the value of x?**

Solution:

Given,

x = cot^{-1}(-âˆš3/3)

We know that cot 2Ï€/3 = -âˆš3/3

x = cot^{-1}(cot 2Ï€/3)

Therefore, x = 2Ï€/3 or x = 120Â°

**Example 2: Find the value of A if A = cot ^{-1}(-1).**

Solution:

Given,

A = cot^{-1}(-1)

We know that cot 3Ï€/4 = -1

A = cot^{-1}(cot 3Ï€/4)

Therefore, A = 3Ï€/4 = 135Â°

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