Re: Re: Simplifying ArcTan

• To: mathgroup at smc.vnet.net
• Subject: [mg55608] Re: [mg55566] Re: Simplifying ArcTan
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 31 Mar 2005 01:23:59 -0500 (EST)
• References: <d2b51c\$79a\$1@smc.vnet.net> <200503300820.DAA21786@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```  It seems that the problem is due  FullSimplify missing a rule.

Note that Mathematica returns:

FullSimplify[Exp[ArcTan[Cos[x], Sin[x]]], -Pi < x < Pi]

E^x

which is equivalent to the expected answer in view of:

Reduce[Exp[x] == Exp[y] && Element[y,Reals], x, Reals]

x == y

Andrzej Kozlowski

On 30 Mar 2005, at 10:20, David W. Cantrell wrote:

> "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
>>
>> 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
>
>

```

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