bug in arccotangent function

10202022, 02:38 PM
Post: #1




bug in arccotangent function
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. 

10202022, 03:27 PM
Post: #2




RE: bug in arccotangent function
I think its not a bug: both results are correct: arccot ist periodical with period pi
Roland 

10202022, 04:44 PM
Post: #3




RE: bug in arccotangent function
(10202022 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 onetoone. 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) ?) 

10202022, 07:22 PM
Post: #4




RE: bug in arccotangent function
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 onetoone relation. Roland 

10202022, 09:44 PM
Post: #5




RE: bug in arccotangent function
I am an engineer ... I thought we were talking about principle branch. :)
acot(x) == atan(1/x) or (pi/2  atan(x)) 

10212022, 01:38 PM
Post: #6




RE: bug in arccotangent function
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 TINspire CX CAS and TI89 Titanium? 

10212022, 05:07 PM
Post: #7




RE: bug in arccotangent function
MATLAB (home use) 0.7854
wxMaxima: pi/4 

10212022, 06:59 PM
Post: #8




RE: bug in arccotangent function
(10212022 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 TINspire CX CAS and TI89 Titanium? Some textbooks define acot(x) as pi/2atan(x) as TI does. This is consistent with acos(x)=pi/2asin(x) and acsc(x)=pi/2asec(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. 

10222022, 01:58 AM
Post: #9




RE: bug in arccotangent function
:(
Thanks to everybody for info. 

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