Re: Re: Simplifying ArcTan

*To*: mathgroup at smc.vnet.net*Subject*: [mg55608] Re: [mg55566] Re: Simplifying ArcTan*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 31 Mar 2005 01:23:59 -0500 (EST)*References*: <d2b51c$79a$1@smc.vnet.net> <200503300820.DAA21786@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

It seems that the problem is due FullSimplify missing a rule. Note that Mathematica returns: FullSimplify[Exp[ArcTan[Cos[x], Sin[x]]], -Pi < x < Pi] E^x which is equivalent to the expected answer in view of: Reduce[Exp[x] == Exp[y] && Element[y,Reals], x, Reals] x == y Andrzej Kozlowski On 30 Mar 2005, at 10:20, David W. Cantrell wrote: > "David Park" <djmp at earthlink.net> wrote: >> I don't know what I was thinking! It should be without the condition >> on >> x. > > Right. The condition that x be nonzero, which you'd mentioned earlier, > was > unnecessary. > >> But why shouldn't >> >> FullSimplify[ArcTan[Cos[x], Sin[x]], >> -Pi < x <= Pi] >> >> simplify to x? After all, the two argument ArcTan works for all >> combinations of arguments, except ArcTan[0, 0] and even that gives >> Interval[{-Pi, Pi}]. >> >> ArcTan[0, 3] >> Pi/2 >> >> In fact, why shouldn't it simplify to x just by specifying that x is >> Real? > > Well, just consider ArcTan[Cos[x], Sin[x]] when x is, say, 2 Pi. > There's > no way that ArcTan[_, _] could yield 2 Pi; it's not in the function's > range. > > If x is merely specified to be Real, then ArcTan[Cos[x], Sin[x]] surely > can't be simplified to anything essentially simpler than the expression > I gave in my previous response. > > David Cantrell > >> David Park >> djmp at earthlink.net >> http://home.earthlink.net/~djmp/ >> >> From: Florian Jaccard [mailto:florian.jaccard at he-arc.ch] To: mathgroup at smc.vnet.net >> >> It does ! >> >> But you have to avoid 2 mistakes : >> >> 1) The brackets on wrong place >> 2) x may not be Pi/2 >> >> In[4]:= >> FullSimplify[ArcTan[Cos[x], Sin[x]], >> x >= 0 && x < Pi/2] >> >> Out[4]= >> x >> >> -----Message d'origine----- >> De : fizzy [mailto:fizzycist at knology.net] >> Envoyé : lun., 28. mars 2005 09:42 >> À : mathgroup at smc.vnet.net >> Objet : Simplifying ArcTan >> >> Why does FullSimplify[ ArcTan[ Cos[x], Sin[x] , x>=0 && x <= Pi/2 ] >> not output x ? >> >> Thanks...jerry blimbaum > >

**References**:**Re: Simplifying ArcTan***From:*"David W. Cantrell" <DWCantrell@sigmaxi.org>