Re: Simplifying ArcTan

*To*: mathgroup at smc.vnet.net*Subject*: [mg55544] Re: Simplifying ArcTan*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Tue, 29 Mar 2005 03:42:28 -0500 (EST)*References*: <d28ftk$n0u$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"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