Which definition of the arccotangent function is correct?

[out of whack]

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?

 

[CRGreathouse]

The Wolfram MathWorld link has the explanation, starting with "There are at least two possible conventions for defining the inverse cotangent."

 

[out of whack]

The Wolfram MathWorld link has the explanation

Doh!