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" <djmp at earthlink.net> wrote: >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[13]*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 >djmp at earthlink.net >http://home.earthlink.net/~djmp/ > > >> 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! >> > >