Re: Simplifying ArcTan

*To*: mathgroup at smc.vnet.net*Subject*: [mg55566] Re: Simplifying ArcTan*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Wed, 30 Mar 2005 03:20:59 -0500 (EST)*References*: <d2b51c$79a$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"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

**Follow-Ups**:**Re: Re: Simplifying ArcTan***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>