Re: Extensive replacement of trigonometric functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg125100] Re: Extensive replacement of trigonometric functions*From*: Mauro <pippo at hotmail.com>*Date*: Tue, 21 Feb 2012 06:15:30 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jhldmn$ouo$1@smc.vnet.net> <jho299$5u6$1@smc.vnet.net>

Thank you, Andr=E9s. Your suggestion is undoubtfully useful for my immediate need of formula visualization, but -more generally- I was looking for a way to direct Mathematica transformations toward some specific desired functions. For example, in this case I would like that simplification process produces Cos functions rather than Sin functions in order to recognize similarities with other expressions. In this case, whenever I try to elaborate an expression such Cos[\[Theta] + \[Alpha]] with \[Alpha] number strictly greater than \[Pi]/4, it will convert to Sin[\[Pi]/2-\[Alpha] - \[Theta]], and I want to avoid this. Anyway, your suggestion is useful, so thank you indeed. Mauro Il 18/02/2012 12:32, andres ha scritto: > So, you don't want Mathematica to evaluate the expression -Cos[\ > [Theta] + (2 \[Pi])/3]? > Since -Cos[\[Theta] + (2 \[Pi])/3] = Sin[\[Theta] + \[Pi]/6], I assume > you want to format the output for visualization purposes, because both > expressions will give the same results. If this is the case, I would > take two approaches: either apply a Hold to the rhs of the rule, or > I'd use a rule of the type Sin[\[Theta]_ + \[Pi]/6] :> -cos[\[Theta] + > (2 \[Pi])/3], so that the inexistent function "cos" keeps unevaluated. > If then you want to evaluate the expression you can release the Hold > or define cos[\[Theta]_] := Cos[\[Theta]]. > Hope it helps. > Andr=E9s > > > > 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 > >