Re: trig expansion

• To: mathgroup at smc.vnet.net
• Subject: [mg9265] Re: trig expansion
• From: murray at math.umass.edu (Murray Eisenberg)
• Date: Fri, 24 Oct 1997 01:01:20 -0400
• Organization: University of Massachusetts, Amherst
• Sender: owner-wri-mathgroup at wolfram.com

```Paul Abbott (paul at physics.uwa.edu.au) wrote:
: 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?

: What is wrong with using a replacment rule?  It is probably the best way
: to achieve what you want here.

Obviously, I'm expecting too much from Mathematica.  For the use I have
in mind (for students who already know the addition formula for Sin), I
would like to be able to tell Mathematica, "Go ahead, use the rule that
expands the Sin of sums" --WITHOUT having to remind it what that rule
is!

: I assume that this question is related to your earlier question (which I
: assume is related to Fourier series expansions?):

Yes, definitely related!

: >I want to make an assignment T = k/omega and somehow cause Mathematica
: >to know that k is an integer.  How do I do this?

: In my opinion, the best way to is using pattern-matching and replacement
: rules (see The Mathematica Journal 2(4): 31).  E.g., for n integral, we
: have

: 	{Cos[(n_)*Pi] -> (-1)^n, Sin[(n_)*Pi] -> 0};

I find that really unpleasant to have to do!  I expect to be able to
tell Mathematica that T = k/omega and that k is an integer and have
*Mathematica* figure out what the Sin and Cos reduce to.

It's all a question of expectation vs. reality of the language design,
of course.  Is my expectation unreasonable?

--
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

```

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