Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun The reciprocal of the tangent of an angle in a right triangle.
 noun The tangent of the complement of a directed angle or arc.
from The Century Dictionary.
 noun In trigonom., the tangent of the complement of a given are or angle. Abbreviated cot. See the figure.
from the GNU version of the Collaborative International Dictionary of English.
 noun (Trig.) The tangent of the complement of an arc or angle. See
Illust. offunctions .
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun trigonometry In a
right triangle , thereciprocal of thetangent of anangle . Symbols:cot , ctg, orctn
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 noun ratio of the adjacent to the opposite side of a rightangled triangle
Etymologies
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Examples

It can also be used for such operations as involution (raising to a power) and evolution (extraction of a root) and for calculations with trigonometric functions (sine, cosine, tangent, cotangent).

Out on the various fronts the American soldiers grimly understood that they must hold on where they were for the sake of their comrades on other distant but nevertheless cotangent fronts on the circular line that guard Archangel.
The History of the American Expedition Fighting the Bolsheviki Campaigning in North Russia 19181919 Harry H. Mead

On this topic, it isn't completely clear to me why we make kids memorize what the secant, cosecant, and cotangent are.

Graph of the cotangent function for values of x between 3 rad and 3 rad.

The curves have the same general shape, but while the tangent function always slopes upward as you move toward the right, the cotangent always slopes downward.

We math majors could write term papers on cotangent bundles and prove the Bolzano Weirstrass theorem, but we don't know jack about T tests or chisquare.
unknown title 2009

Shit I forgot a dino egg guess cotangent did not want to hatch guess I will have to fix that
Transformers News 2009

The graph of the cotangent function looks similar to that of the tangent function.

If we are operating on some variable x, the arccotangent of x is denoted cotÀ1 (x) or arccot (x) The sine, cosine, tangent, cosecant, secant, and cotangent require special restrictions in order for the inverses to be de ﬁ nable as legitimate functions.

The Right Triangle Model In the previous chapter, we de ﬁ ned the six circular functionssine, cosine, tangent, cosecant, secant, and cotangentin terms of points on a circle.
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