[Octave-bug-tracker] [bug #59774] The function acot(x) seems to compute the wrong number for x<0.

[Rik]

Update of bug #59774 (project octave):

                  Status:                    None => Invalid                
             Open/Closed:                    Open => Closed                 
        Operating System:       Microsoft Windows => Any                    

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Follow-up Comment #1:

Octave is correct, or at least follows other numerical analysis packages.

On the Wikipedia page you cite, see the section "Relationships between
trigonometric functions and inverse trigonometric functions".  There, you will
find the relationship


tan (arccot (x)) = 1/x
+verbatim-

Apply arctan() to both sides of the equation and the result is


arctan (tan (arccot (x))) = arctan (1/x)
===
arccot (x) = arctan (1/x)


For a test, try


acot (-1)


In Octave, Matlab, and Mathematica this returns -pi/4.  Under your scheme the
result is 3/4pi which is different on both the sign and the value.


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