RE: Rewriting of Trigonometric Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg26827] RE: [mg26803] Rewriting of Trigonometric Functions*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 25 Jan 2001 01:13:09 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Thomas, ?TrigReduce "TrigReduce[expr] rewrites products and powers of trigonometric functions in \ expr in terms of trigonometric functions with combined arguments." Sin[a]^2 TrigReduce[%] Sin[a]^2 1/2*(1 - Cos[2*a]) Sin[a]Sin[b] % // TrigReduce Sin[a] Sin[b] 1/2*(Cos[a - b] - Cos[a + b]) David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > From: Thomas Engelhardt [mailto:thomas-a.engelhardt at t-online.de] To: mathgroup at smc.vnet.net > Dear Mathgroup members, > > I have just started to use Mathematica and directly ran into a problem: > > I have rather lengthy expressions resulting from putting a sum of two > sinusodial swings to the power of three (Two-tone Intermodulation). > In order for me to recognise the contained frequencies I want > Mathematica to > rewrite the contained Trigonometric functions in certain ways, > namely like: > > [sin(a)]^2 should be transformed into 1/2*(1+cos2x) > and for higher powers accordingly. > > Furthermore: > sin(a)*sin(b) should be changed to 1/2*[cos(a-b) - cos(a+b)] > > I have tried all kinds of "Expand" and "Trig..." operations but > Mathematica > always keeps the powers on the trigonometric functions and doesn't change > the multiplications either. > > Does anybody have an idea how I can get Mathematica to transform the > expressions in the desired way? > > I appreciate your help! > Thanks in advance. > > Kind Regards > > Thomas > Munich, Germany > > >