Which definition of the arccotangent function is correct?

In summary, there are multiple sources that provide information on the arccotangent function, including Wikipedia, Cliffsnotes, Wolfram and Mathlab. However, there are different conventions for defining the inverse cotangent, with some references adding PI on the negative side and others not. The Wolfram MathWorld link offers an explanation for these differing conventions.
  • #1
out of whack
436
0
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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  • #2
The Wolfram MathWorld link has the explanation, starting with "There are at least two possible conventions for defining the inverse cotangent."
 
  • #3
CRGreathouse said:
The Wolfram MathWorld link has the explanation
:redface: Doh!
 

What is the inverse cotangent function?

The inverse cotangent function, denoted as cot-1(x) or arccot(x), is the inverse of the cotangent function. It gives the angle in radians that has a given cotangent value. In other words, it is the function that "undoes" the cotangent function.

What is the domain and range of the inverse cotangent function?

The domain of the inverse cotangent function is (-∞, ∞), meaning it can take any real number as its input. The range of the inverse cotangent function is (-π/2, π/2), which corresponds to the values between -90° and 90° in degrees.

How is the inverse cotangent function related to the cotangent function?

The inverse cotangent function is the inverse of the cotangent function, meaning that the composition of the two functions results in the input value. In other words, if we take the cotangent of an angle, and then take the inverse cotangent of that result, we will get back the original angle.

What are the properties of the inverse cotangent function?

The inverse cotangent function is an odd function, meaning that cot-1(-x) = -cot-1(x). It is also a monotonic function, meaning that it always increases or decreases, and is continuous on its entire domain.

How is the inverse cotangent function used in real life?

The inverse cotangent function is used in fields such as engineering, physics, and navigation. It can be used to calculate the angle of a right triangle if the length of the adjacent and opposite sides are known. It is also used in signal processing and in the calculation of resonance in electrical circuits.

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