MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: How to simplify ArcSin formula

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123388] Re: How to simplify ArcSin formula
  • From: Dana DeLouis <dana01 at me.com>
  • Date: Mon, 5 Dec 2011 05:15:18 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

...with  -1 < aa < 1
...The answer I know is xxx = 0

Hi.  Given a value of aa, the return value is 0 only when 
t falls within a certain range. 

RangeOfT[aa_] := Interval[{-Pi + ArcCos[aa], ArcCos[aa]}]

So, if aa were 1/2.

RangeOfT[1/2]
Interval[{-((2*Pi)/3), Pi/3}]

RangeOfT[1/2] //N
Interval[{-2.094, 1.047}]

If given aa as 1/2, then the equation is zero only when t is between
-2.094 and 1.047


Chop[xxx /. {aa -> 1/2, t -> 1.04}]
0

Chop[xxx /. {aa -> 1/2, t -> 1.05}]
0.0056048976068160394

= = = = = =
HTH
Dana DeLouis
= = = = = =



On Nov 29, 7:06 am, David Sagan <david.sa... at gmail.com> wrote:
> 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:
>   FullSimplify[xxx, -1<a<1]
> but that did not work. Can anyone tell me how to do this?
> 
> -- Thanks, David





  • Prev by Date: Re: How to get elements satisfying specific condition from a list
  • Next by Date: Need help integrating Wolfram Alpha data in Mathematica
  • Previous by thread: Re: How to simplify ArcSin formula
  • Next by thread: Re: gives different result compared to 1/Diagonal[Normal@A] when A is sparse