Re: Trig Simplifications

• To: mathgroup at smc.vnet.net
• Subject: [mg3707] Re: Trig Simplifications
• From: ianc (Ian Collier)
• Date: Wed, 10 Apr 1996 02:11:22 -0400
• Organization: Wolfram Research, Inc.
• Sender: owner-wri-mathgroup at wolfram.com

```In article <4ka54g\$sai at dragonfly.wolfram.com>, Alexander Casti
<arc at carmen.phys.columbia.edu> wrote:

> Basically my question is how to get mathematica to write
>
> Exp[I x] in place of Cos[x] + I Sin[x]
>
> Suppose I have the expression
>
> In[1]: f[x_]= Cos[x] + I Sin[x] - Cos[2 X] + I Sin[2 X]
>
> I would like mathematica to simplify this into
>
> f[x_]= Exp[I X] - Exp[2 I X]
>
> I tried the substitution command
>
> In[2]: % ./ Cos[X]+I Sin[X]-> Exp[I X] and it returned
> Out[2]: E^{I X}  - Cos[2 X] + I Sin[2 X]
>
> So, it seems as though this simple minded approach is not
> enough for mathematica to understand the substitution rules
> for powers of complex exponentials other than the one I
> explicitly gave.
> In addition, commands like Simplify[Blah] do not seem to do
> the trick either.  I believe I have the trigonometry package
> loaded in (via the command Needs["Algebra`Trigonometry`"]).
> What must I do ?
>
>
> Alex

You can do this using the function TrigToComplex which
is defined in Algebra`Trigonometry`, one of the standard
packages distributed with Mathematica. Here is an example:

In[1]:=
Needs[ "Algebra`Trigonometry`" ]

In[2]:=
expr = Cos[x] + I Sin[x]
Out[2]=
Cos[x] + I Sin[x]

In[3]:=
TrigToComplex[ expr ]
Out[3]=
-I x    I x    -I x    I x
-E     + E      E     + E
------------- + ------------
2              2

In[4]:=
Simplify[%]
Out[4]=
I x
E

This is documented in more detail on pages 15-17 of "The
Guide to Standard Mathematica Packages" Technical Report.

I hope this helps.

--Ian

-----------------------------------------------------------
Ian Collier
Wolfram Research, Inc.
-----------------------------------------------------------
tel:(217) 398-0700   fax:(217) 398-0747    ianc at wolfram.com