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MathGroup Archive 1997

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Re: trig expansion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8956] Re: trig expansion
  • From: tburton at cts.com (Tom Burton)
  • Date: Mon, 6 Oct 1997 01:59:24 -0400
  • Organization: Brahea Consulting
  • Sender: owner-wri-mathgroup at wolfram.com

On 30 Sep 1997 19:05:29 -0400, in comp.soft-sys.math.mathematica you
wrote:

>How can I cause Mathematica to expand Sin[2 Pi omega t + 2 Pi delta],
>where delta and omega are symbols, into the form
>
>   Cos[2 Pi delta] Sin[2 Pi omega t] + Sin[2 Pi delta] Cos[2 Pi omega t]
>
>without using a replacment rule=20
>
>    Sin[a_ + b_] -> Sin[a]Cos[b] + Cos[a]Sin[b]
>
>explicitly?  (No TrigExpand does NOT do the trick -- it expands all
>the way down to trig functions of Pi delta and Pi t omega!)

Here's a solution that appears to be a bit more general than those I've
seen posted so far. The notion is to temporarily denature Times to foil
TrigExpand:


In[40]:=3D TrigExpand[Sin[a x + b y + c d z]
             /.HoldPattern[Times[p__]]:>TimesHold[p]]
           /.TimesHold[p__]:>Times[p]
Out[40]=3D
Cos[b y] Cos[c d z] Sin[a x]+Cos[a x] Cos[c d z] Sin[b y]+
  Cos[a x] Cos[b y] Sin[c d z]-Sin[a x] Sin[b y] Sin[c d z]
Tom Burton


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