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)
• 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
>
>

```

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