Which definition of the arccotangent function is correct?

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The discussion centers on the differing definitions of the arccotangent function, particularly regarding the inclusion of π in negative values. Some sources, like Wikipedia and CliffsNotes, present a definition where arccot(-x) = π - arccot(x), while others, such as Wolfram and Mathlab, define it as arccot(x) = arctan(1/x). This discrepancy raises questions about which convention is more accurate. The Wolfram MathWorld source acknowledges that there are multiple conventions for defining the inverse cotangent. Ultimately, the choice of definition may depend on the specific mathematical context or application.
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Wikipedia shows this graph for the arccotangent function, which I can also find in a few other web pages like http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Other-Inverse-Trigonometric-Functions.topicArticleId-11658,articleId-11641.html.

On the other hand I have these from Wolfram and Mathlab.

Why do some references add PI on the negative side while others do not? I see definitions for negative values such as arccot(-x) = pi - arccot(x) in the first case and arccot(x) = arctan(1/x) for the second case. Which one is (more) correct?
 
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The Wolfram MathWorld link has the explanation, starting with "There are at least two possible conventions for defining the inverse cotangent."
 
CRGreathouse said:
The Wolfram MathWorld link has the explanation
:redface: Doh!
 

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