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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]
>
> - - - - - - - - - - - - - - - - - - - - - -
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