Re: Simplifying ArcTan
- To: mathgroup at smc.vnet.net
- Subject: [mg55552] Re: Simplifying ArcTan
- From: "fizzy" <fizzycist at knology.net>
- Date: Tue, 29 Mar 2005 03:42:34 -0500 (EST)
- References: <20050328090641.635$0N@newsreader.com>
- Sender: owner-wri-mathgroup at wolfram.com
Let me add....if you do Arg[ Exp[ i Pi/2]] you get Pi/2......that was why I included it in the range of allowed values for x jerry blimbaum ----- Original Message ----- From: "David W. Cantrell" <DWCantrell at sigmaxi.org> To: mathgroup at smc.vnet.net Subject: [mg55552] Re: Simplifying ArcTan > "Florian Jaccard" <florian.jaccard at he-arc.ch> wrote: >> 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 > > You say that "x may not be Pi/2". Apparently that is true if Mathematica > is > to do the simplification now. But there's no mathematical reason we should > have to exclude x = Pi/2. Even Mathematica knows that, at x = Pi/2, > ArcTan[Cos[x], Sin[x]] is the same as x: > > In[5]:= ArcTan[Cos[x], Sin[x]] /. x -> Pi/2 > > Out[5]= Pi/2 > > Indeed, it would surely be desirable if Mathematica simplified > ArcTan[Cos[x], Sin[x]] to x whenever -Pi < x <= Pi. > > More generally, we may simplify ArcTan[Cos[x], Sin[x]] to an expression > involving no trig or inverse trig functions > > x + 2 Pi Floor[1/2 - x/(2 Pi)] > > for all real x. > > David Cantrell > > >> -----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 > >