       Re: Wrestling with Mathematica on Trig Simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg32247] Re: Wrestling with Mathematica on Trig Simplification
• From: rlsmith at his.com (Poppo)
• Date: Wed, 9 Jan 2002 03:17:59 -0500 (EST)
• References: <a1bllp\$bcb\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Why write m[a_,b_][t_] instead of m[a_,b_,t_]?

On Mon, 7 Jan 2002 08:19:05 +0000 (UTC), "David Park"

>Steven,
>
>I think this may be a good example of what often happens with Mathematica.
>Users, especially new users, expect and hope that there will be off the
>shelf Mathematica commands to directly solve their problem. But mathematics
>is too vast a subject for that without having millions of commands (which
>would present a problem in itself). Often, very often, you are going to have
>to write definitions, rules and small routines to use as tools in your
>specific application. One should view Mathematica more as a kit to build
>tools than as a ready-to-use problem solver.
>
>For you problem I would write the initial definition this way:
>
>m[a_, b_][t_] := a Sin[t] + b Cos[t]
>
>Then, checking with my favorite Mathematics Handbook, I would write the
>amplitude-phase angle conversion as:
>
>AmplitudePhaseSimplify[expr_] :=
>  expr /. (a_.)*Sin[t_] + (b_.)*Cos[t_] ->
>    Sqrt[a^2 + b^2]*Cos[t - ArcTan[a/b] -
>       If[a < 0, Pi, 0]]
>
>Since it has an If statement in it, it doesn't look too great with symbolic
>expressions. But with number expressions it works nicely.
>
>m[3, 2][t]
>% // AmplitudePhaseSimplify
>2 Cos[t] + 3 Sin[t]
>Sqrt*Cos[t - ArcTan[3/2]]
>
>Of course, sometimes one later finds that Mathematica does have a direct way
>to do it, and you might even get such a reply from MathGroup.
>
>David Park
>
>
>> From: Steven Warwick [mailto:warwick at jps.net]
To: mathgroup at smc.vnet.net
>>
>> So, A typical scenario for me is the combining of sinusoids like:
>>
>> m[t_]  = A Sin[t] + B Cos[t]
>>
>> ( A and B Real, although I don't know how to communicate this to
>> Mathematica
>> in an effective way)
>>
>> with the desired "simplified" output being of the form:
>>
>> C  Cos[t+th]
>>
>>
>> Trigreduce will not do this, as I've tried. Yes, C and th are more
>> algebraically complicated, but the overall expression is actually more
>> meaningful for me..
>>
>> I can solve for C and th using Solve, with creating 2 simultaneous
>> equations with t picked at 0, PI/2 to get the correct form, but that's
>> not the same as having a "reduce" capability.   Am I missing
>> something? is there a way to create preference for this form in
>> simplify?
>>
>> Thanks!
>>
>
>

```

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