Re: Wrestling with Mathematica on Trig Simplification

*To*: mathgroup at smc.vnet.net*Subject*: [mg32392] Re: Wrestling with Mathematica on Trig Simplification*From*: adam.smith at hillsdale.edu (Adam Smith)*Date*: Fri, 18 Jan 2002 00:17:38 -0500 (EST)*References*: <a1bllp$bcb$1@smc.vnet.net> <a1qrr1$9ee$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Dana, Your method seems very elegant to me. In fact if a and b (or any other variables are assumed to be real you can get it to very nicely simplify by using complex expand. A comparison is below. I also used some of the ideas from David Park's previous posts to this question. In[1]:= oldrule[expr_] := expr/. a_ Sin[t_] + b_ Cos[t_] -> Abs[a + b I]Cos[t - Arg[b + I a]] In[2]:= oldrule[2 Cos[t]+3 Sin[t]] oldrule[a Cos[t]+b Sin[t]] Out[2]= Sqrt[13]*Cos[t - ArcTan[3/2]] Out[3]= Abs[I*a + b]*Cos[t - Arg[a + I*b]] In[4]:= newrule[expr_] := ComplexExpand[ expr/. a_ Sin[t_] + b_ Cos[t_] -> Abs[a + b I]Cos[t - Arg[b + I a]] , TargetFunctions->{Re,Im}] In[5]:= newrule[2 Cos[t]+3 Sin[t]] newrule[a Cos[t]+b Sin[t]] Out[5]= Sqrt[13]*Cos[t - ArcTan[3/2]] Out[6]= Sqrt[a^2 + b^2]*Cos[t - ArcTan[a, b]] Adam Smith "Dana" <ng_only at hotmail.com> wrote in message news:<a1qrr1$9ee$1 at smc.vnet.net>... > I am really new at this, so I am probably way off. Taking your excellent > idea, perhaps you could rewrite it as the following rule?? > > myrule = a_ Sin[t_] + b_ Cos[t_] -> Abs[a + b I]Cos[t - Arg[b + I a]] > > As an example: > > In[5]:= > 3Sin[1/2]+4Cos[1/2]/.myrule > > Out[5]= > 5*Cos(1/2 - ArcTan(3/4)) > > On could include this following in Mathematica 4 to set a & b to Reals. > Element[{a, b}, Reals] > > - - - - - - - - - - - - - - - - - - - - - -