Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

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

Search the Archive

Re: question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77848] Re: question
  • From: roland franzius <roland.franzius at uos.de>
  • Date: Mon, 18 Jun 2007 06:58:54 -0400 (EDT)
  • Organization: Universitaet Hannover
  • References: <f5338c$3pc$1@smc.vnet.net>

dimitris wrote:
> Two eforts in Mathematica 5.2 in order
> to simplify o below
> 
> o = 2*Cos[Pi/48]*(1 - Cos[Pi/48]^2)^(1/2) + 2*Cos[Pi/48]^2 - 1;
> 
> First leaving Mathematica do the job.
> 
> Timing[ToRadicals[RootReduce[(FullSimplify[#1, ComplexityFunction ->
> (Count[{#1}, _Cos, Infinity] & )] & )[o]]]]
> {43.031*Second, Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])]}
> 
> Then help a bit Mathematica.
> I couldn't find a built in command to simplify 1 - Cos[Pi/48]^2 to
> Sin[Pi/48]^2. That's why the adding of a rule.
> 
> Timing[ToRadicals[RootReduce[Simplify[o /. 1 - Cos[Pi/48]^2 ->
> Sin[Pi/
> 48]^2]]]]
> {0.25*Second, Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])]}
> 
> Any other suggestions will be highly appreciated.


Timing[o // TrigToExp // FullSimplify]

{8.512*Second, (1/2)*Sqrt[4 - Sqrt[2] + Sqrt[6]]}

Timing[o /. Cos[x_] :> 1/Sqrt[1 + Tan[x]^2] // FullSimplify]

{0.631*Second, (1/2)*Sqrt[4 - Sqrt[2] + Sqrt[6]]}




-- 

Roland Franzius


  • Prev by Date: Rule and Module not working together
  • Next by Date: Re: question
  • Previous by thread: Re: question
  • Next by thread: Re: question