bug in arccotangent function - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: bug in arccotangent function (/thread-18989.html) bug in arccotangent function - gor1060 - 10-20-2022 02:38 PM Hello! i have found bug in arccotangent function for both Home and Cas modes. For example, acot(-1)=-pi/4 that is wrong because acot(-1)=3pi/4. The same behaviour exists for Xcas and Wolfram Alpha. RE: bug in arccotangent function - Roland57 - 10-20-2022 03:27 PM I think its not a bug: both results are correct: arccot ist periodical with period pi Roland RE: bug in arccotangent function - Albert Chan - 10-20-2022 04:44 PM (10-20-2022 03:27 PM)Roland57 Wrote:  I think its not a bug: both results are correct: arccot ist periodical with period pi You cannot have *both* right, since acot is one to one function. It is just software packages may have different definition of acot. Once defined, it is always one-to-one. I prefer Mathematica's definition of acot(x) as odd function, even though curve has a discontinuity at 0. see thread What should be the correct range of acot function BTW, acot(x) is not periodic. (may be you meant cot(x) ?) RE: bug in arccotangent function - Roland57 - 10-20-2022 07:22 PM I'm a physicist, not a mathematician, I have a very practical look at this problem :-) cot(-pi/4) equals cot(3pi/4) = -1 therefore, arccot(-1) has many solutions, among many others the above mentioned two. And yes: cot() ist periodic and (for a physicist) arccot() ist not a one-to-one relation. Roland RE: bug in arccotangent function - Albert Chan - 10-20-2022 09:44 PM I am an engineer ... I thought we were talking about principle branch. :-) acot(x) == atan(1/x) or (pi/2 - atan(x)) RE: bug in arccotangent function - gor1060 - 10-21-2022 01:38 PM Ok. Thanks. Then another question: Why does HP Prime as educational tool have another definition of arccotangent function opposite to such global educational tools as TI-Nspire CX CAS and TI-89 Titanium? RE: bug in arccotangent function - klesl - 10-21-2022 05:07 PM MATLAB (home use) -0.7854 wxMaxima: -pi/4 RE: bug in arccotangent function - Wes Loewer - 10-21-2022 06:59 PM (10-21-2022 01:38 PM)gor1060 Wrote:  Why does HP Prime as educational tool have another definition of arccotangent function opposite to such global educational tools as TI-Nspire CX CAS and TI-89 Titanium? Some textbooks define acot(x) as pi/2-atan(x) as TI does. This is consistent with acos(x)=pi/2-asin(x) and acsc(x)=pi/2-asec(x). Other textbooks define acot(x) as atan(1/x) as HP does. This is consistent with asec(x)=acos(1/x) and acsc(x)=asin(1/x). Unfortunately, there is no consensus in the educational world as to the "correct" one. RE: bug in arccotangent function - gor1060 - 10-22-2022 01:58 AM :-( Thanks to everybody for info.