Which definition of the arccotangent function is correct?

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SUMMARY

The arccotangent function has multiple definitions, leading to confusion regarding its representation. Some sources, such as Wikipedia and CliffsNotes, define arccot(-x) as π - arccot(x), while others, including Wolfram and MATLAB, define it as arccot(x) = arctan(1/x). The discrepancy arises from different conventions in defining the inverse cotangent function, with Wolfram MathWorld providing a comprehensive explanation of these conventions.

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  • Research the conventions of inverse trigonometric functions in mathematical literature
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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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