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

[anonymous]

URL:
  <https://savannah.gnu.org/bugs/?59774>

                 Summary: The function acot(x) seems to compute the wrong
number for x<0.
                 Project: GNU Octave
            Submitted by: None
            Submitted on: Mon 28 Dec 2020 10:58:47 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: Imre Patyi
        Originator Email: patyii@ecu.edu
             Open/Closed: Open
                 Release: 5.2.0
         Discussion Lock: Any
        Operating System: Microsoft Windows

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Details:

Dear Octave,

Thank you for making your program available.

I think the function acot whose source code we can see by typing type acot
does not produce the mathematically expected results for negative argument.

You basically have

acot=@(x)atan(1./x) ;

whereas I think you should have

acot=@(x)pi/2-atan(x) ;

See wikipedia, 
https://en.wikipedia.org/wiki/Inverse_trigonometric_functions

for a picture of the graph of

plot(x=linspace(-3,3,1000),acot(x))

and compare it to the one Octave (5.2.0, Windows) produces.

Thank you very much!

Yours sincerely,
Imre Patyi





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