       Re: Re: Simplifying ArcTan

• To: mathgroup at smc.vnet.net
• Subject: [mg55554] Re: [mg55541] Re: [mg55526] Simplifying ArcTan
• From: "David Park" <djmp at earthlink.net>
• Date: Tue, 29 Mar 2005 03:42:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```I don't know what I was thinking! It should be without the condition on x.

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?

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 : [mg55526] 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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