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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
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