       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
>
> 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:=
> FullSimplify[ArcTan[Cos[x], Sin[x]],
>   x >= 0 && x < Pi/2]
>
> Out=
> 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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