Re: General--Trigonometric functions manipulations in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg71508] Re: General--Trigonometric functions manipulations in Mathematica*From*: "ben" <benjamin.friedrich at gmail.com>*Date*: Tue, 21 Nov 2006 07:05:05 -0500 (EST)*References*: <ejtdp7$j4f$1@smc.vnet.net>

Hi Ali TrigReduce might be what you want; TrigExpand TrigToExp TrigFactor also come in handy quite regularly. If everything fails, try to specify substitution rules explicitly, i.e. exp/.{Cos[a__]^2+Sin[a__]^2->1} Bye Ben ali.abuelmaatti at elec.gla.ac.uk schrieb: > Hi all, > > I am trying to perform the following operation: > > Let us assume I have a two-tone input to my system in the form > > x = A Sin[Ω1] + A Sin[Ω2] > > and our system is nonlinear so it looks like this > > y = x + x2 + x3 > > Now to substitute x (the input) into y (the system) I use the expand function as follows > > Expand [y] > > Out[1]= ASin[Ω1] + A2Sin[Ω1] 2 + A3 Sin[Ω1]3 + A Sin[Ω2] + 2A2 Sin[Ω1] Sin[Ω2] + 3A3 Sin[Ω1]2 Sin[Ω2] + A2 Sin[Ω2]2 + 3A3 Sin[Ω1] Sin[Ω2]2 + A3 Sin[Ω2]3 > > Now that is good as it is substituted properly but this is just direct substitution and it is not what I am looking for, I want to break all the high power terms on the Sin functions so I try using simplify as follows: > > Simplify[Out[1]] > > Out[2]= A (Sin[Ω1] + Sin[Ω2]) (1 + A2 Sin[Ω1]2 + A Sin[Ω2] + A2 Sin[Ω2]2 + A Sin[Ω1] (1 + 2A Sin[Ω2])) > > Now it looks better but unfortunately it doesnÂ?t get a lot further than that. > > The question is, how can I persuade Mathematica to use some of the well known trigonometric functions for example: > > Sin[Ω1+ Ω2]=Sin[Ω1] Cos[Ω2] + Cos[Ω1] Sin[Ω2], > > Sin[Ω1- Ω2]=Sin[Ω1] Cos[Ω2] - Cos[Ω1] Sin[Ω2], > > Cos[Ω1+ Ω2]= Cos[Ω1] Cos[Ω2] - Sin[Ω1] Sin[Ω2], > > Cos[Ω1- Ω2]= Cos[Ω1] Cos[Ω2] + Sin[Ω1] Sin[Ω2], > > Cos[Ω1]2=.5 + .5 Cos[2Ω1] > > And > > Cos[Ω1]2=.5 - .5 Cos[2Ω1] > > To produce the terms that has [Ω1+ Ω2], [Ω1+ Ω2], [2Ω1] or [2Ω2]. These are the terms that I am most interested it which do come out of that non linear system when fed with a two-tone input. > > Which functions can I use to give me that, give me these Sin or Cos [Ω1+ Ω2], [Ω1+ Ω2], [2Ω1] or [2Ω2] terms? > > Thanks all in advance for reading and for your help. > > Ali > > > Link to the forum page for this post: > http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Special:Forum_ViewTopic&pid=15508#p15508 > Posted through http://www.mathematica-users.org [[postId=15508]]