Re: trig expansion

• To: mathgroup at smc.vnet.net
• Subject: [mg8911] Re: [mg8854] trig expansion
• From: Daniel Lichtblau <danl>
• Date: Thu, 2 Oct 1997 22:57:04 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Murray Eisenberg 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
>
>     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!)
>
> --
>   Murray Eisenberg                       Internet:  murray at math.umass.edu
>   Mathematics & Statistics Dept.            Voice:  413-545-2859 (W)
>   University of Massachusetts                       413-549-1020 (H)
>   Amherst, MA 01003                           Fax:  413-545-1801

One method is to temporarily replace integer coefficients (or to replace
them temporarily, if you prefer not to split an infinitive). A
quick-and-dirty approach is below.

In[34]:= ee =  Sin[2 Pi omega t + 2 Pi delta];

In[35]:= rule1 = a_Integer :> int[a];

In[36]:= rule2 = int[a] :> a;

In[37]:= (TrigExpand[ee /. rule1]) /. rule2
Out[37]= Cos[omega Pi t int[2]] Sin[delta Pi int[2]] +
>    Cos[delta Pi int[2]] Sin[omega Pi t int[2]]

More generally you may want to handle rational and Gaussian
coefficients, as these are the multipliers of interest to TrigExpand.

Daniel Lichtblau
Wolfram Research
danl at wolfram.com

```

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