Re: Extensive replacement of trigonometric functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg125153] Re: Extensive replacement of trigonometric functions*From*: Dana DeLouis <dana01 at me.com>*Date*: Sat, 25 Feb 2012 01:53:16 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

> Regretfully, the application of the rules: > > Sin[\[Theta]_ + \[Pi]/6] -> -Cos[\[Theta] + (2 \[Pi])/3] > Sin[\[Theta]_ - \[Pi]/6] -> Cos[\[Theta] - (2 \[Pi])/3] > > results in a flop, since sine functions stubbornly appear again! Hi. I don't have a good solution, but perhaps a workaround using HoldForm... Here's a made up equation with both of your Sin examples. equ = (Sin[x + Pi/6] + 3*Tan[x] + Sqrt[2]) / (Cos[x - 1/2] + Sin[x - Pi/6]); I used just 1 rule for Sin vs your 2 rules. rule1 = Sin[x___]:>cos[Pi/2-x]; rule2 = cos[x___]:>HoldForm[Cos[x]]; equ /.rule1 /.rule2 (Sqrt[2]+Cos[Pi/3-x]+3 Tan[x]) / (Cos[1/2-x]-Cos[Pi/3+x]) To go back to using Sin, use: ReleaseHold[%] The following -- almost worked--, but it didn't simplify the terms inside the function. I don't know why. NoSin[e_]:=100*Count[e,_Sin,{0,Infinity}] FullSimplify[equ, ComplexityFunction -> NoSin] (Sqrt[2]+Cos[1/3 (Pi-3 x)]+3 Tan[x])/(Cos[1/2 (1-2 x)]-Cos[1/3 (Pi+3 x)]) = = = = = = = = = = = = HTH :>) Dana DeLouis Mac, Math 8.0 = = = = = = = = = = = = On Feb 17, 6:29 am, Mauro <pi... at hotmail.com> wrote: > Hello to everybody. > > I have this problem: I would like to replace in a long expression all > the occurrences of: > > Sin[\[Theta]_ + \[Pi]/6] and Sin[\[Theta]_ - \[Pi]/6] > > with respectively: > > -Cos[\[Theta] + (2 \[Pi])/3] and Cos[\[Theta] - (2 \[Pi])/3] > > (which actually are the same thing). > Regretfully, the application of the rules: > > Sin[\[Theta]_ + \[Pi]/6] -> -Cos[\[Theta] + (2 \[Pi])/3] > Sin[\[Theta]_ - \[Pi]/6] -> Cos[\[Theta] - (2 \[Pi])/3] > > results in a flop, since sine functions stubbornly appear again! > > Can you help me? > > Thank you in advance > > Mauro