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Re: General--Trigonometric functions manipulations in Mathematica


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]]


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