**Inverse Cotangent**

cot^{-1} | ctg^{-1} |

Cot^{-1} | Ctg^{-1} |

arccot | arcctg |

Arccot | Arcctg |

The inverse function of cotangent.

**Basic idea**: To find cot^{-1} 1, we ask "what angle has cotangent equal to 1?" The answer is 45°. As a result we say ^{-1} 1 = 45°.^{-1} 1 = π/4.

**More**: There are actually many angles that have cotangent equal to 1. We are really asking "what is the simplest, most basic angle that has cotangent equal to 1?" As before, the answer is 45°. Thus ^{-1} 1 = 45°^{-1} 1 = π/4.

**Details**: What is cot^{-1} (–1)? Do we choose 135°, –45°, 315°, or some other angle? The answer is 135°. With inverse cotangent, we select the angle on the top half of the unit circle. Thus ^{-1} (–1) = 135°^{-1} (–1) = 3π/4.

In other words, the range of ^{-1}^{-1}

Note: arccot refers to "arc cotangent", or the radian measure of the arc on a circle corresponding to a given value of cotangent.

__Technical note__: Since none of the six trig functionssine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Cot or ^{-1}).

**See also**

Inverse trigonometry, inverse trig functions, interval notation

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