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Re: Re: Re: Simplifying ArcTan

• To: mathgroup at smc.vnet.net
• Subject: [mg55613] Re: [mg55567] Re: [mg55542] Re: [mg55526] Simplifying ArcTan
• From: DrBob <drbob at bigfoot.com>
• Date: Thu, 31 Mar 2005 01:24:12 -0500 (EST)
• References: <200503300821.DAA21790@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

> ArcTan[Cos[x],Sin[x]] == x

The RHS function is one-to-one, but the LHS is periodic in x. They only agree on an interval.

Bobby

On Wed, 30 Mar 2005 03:21:00 -0500 (EST), David Park <djmp at earthlink.net> wrote:

> But why this restriction? I thought the whole point of the two argument
> ArcTan was that it covered the entire circle, taking signs into account. The
> two argument ArcTan is a great idea that is incorporated into Mathematica.
> It would be even greater if Simplify knew the identity...
>
> ArcTan[Cos[x],Sin[x]] == x
>
> Is there any reason that should not be true?
>
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
>
>
> From: Bob Hanlon [mailto:hanlonr at cox.net]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
>
>
> Simplify[ArcTan[Cos[x],Sin[x]],0<=x<Pi/2]
>
> x
>
>
> Bob Hanlon
>
>
>
>
>
>



-- 
DrBob at bigfoot.com

• References:
  • Re: Re: Simplifying ArcTan
    • From: "David Park" <djmp@earthlink.net>