Re: How to simplify ArcSin formula
- To: mathgroup at smc.vnet.net
- Subject: [mg123303] Re: How to simplify ArcSin formula
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 1 Dec 2011 05:49:19 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201111301205.HAA19862@smc.vnet.net>
You are making several assumptions which hide the actual complexity of
the situation. The expression is only zero for a certain range of
parameter values, as can be clearly seen from this graph:
Plot3D[Chop[
t + ArcSin[aa] -
ArcSin[aa Cos[t] + Sqrt[1 - aa^2] Sin[t]]], {t, -Pi/2,
Pi/2}, {aa, -1, 1}, AxesLabel -> {"t", "aa", "x"}]
Andrzej Kozlowski
On 30 Nov 2011, at 13:05, Alexei Boulbitch wrote:
> Hi, David,
>
>
>
> You should help Mathematica understanding what you would like to get.
I would do it like follows:
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>
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> xxx = t + ArcSin[aa] - ArcSin[aa Cos[t] + Sqrt[1 - aa^2] Sin[t]];
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>
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> xxx1 = xxx /. aa -> Sin[\[CurlyPhi]] /.
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> Sqrt[1 - Sin[\[Alpha]_]^2] -> Cos[\[Alpha]]
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> This gives you
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>
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> t + ArcSin[Sin[\[CurlyPhi]]] -
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> ArcSin[Cos[\[CurlyPhi]] Sin[t] + Cos[t] Sin[\[CurlyPhi]]]
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>
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> Then make
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>
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> Simplify[xxx1] /. ArcSin[Sin[\[Alpha]_]] -> \[Alpha]
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> Giving you 0.
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> Have fun, Alexei
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>
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> I am trying to discover how to simplify xxx where xxx is defined to
>
> be:
>
> xxx= t + ArcSin[aa] - ArcSin[aa Cos[t] + Sqrt[1 - aa^2] Sin[t]]
>
> with
>
> -1 < aa < 1
>
> The answer I know is xxx = 0 but the reason I am posing the question
>
> is that I am interested in finding out, in general, how to manipulate
>
> formulas of this type. I tried:
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> FullSimplify[xxx, -1<a<1]
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> but that did not work. Can anyone tell me how to do this?
>
>
>
> -- Thanks, David
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>
>
>
>
> Alexei BOULBITCH, Dr., habil.
>
> IEE S.A.
>
> ZAE Weiergewan,
>
> 11, rue Edmond Reuter,
>
> L-5326 Contern, LUXEMBOURG
>
>
>
> Office phone : +352-2454-2566
>
> Office fax: +352-2454-3566
>
> mobile phone: +49 151 52 40 66 44
>
>
>
> e-mail: alexei.boulbitch at iee.lu<mailto:alexei.boulbitch at iee.lu>
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