Re: Question : How to force ( Exp[I x]/2+Exp[-I x]/2=cos(x) ) ?
- To: mathgroup at smc.vnet.net
- Subject: [mg3403] Re: Question : How to force ( Exp[I x]/2+Exp[-I x]/2=cos(x) ) ?
- From: ianc (Ian Collier)
- Date: Mon, 4 Mar 1996 02:34:44 -0500
- Organization: Wolfram Research, Inc.
- Sender: owner-wri-mathgroup at wolfram.com
In article <4hbgms$4uu at dragonfly.wolfram.com>, yjtsai at leland.Stanford.EDU
(Yeou-Jyh Tsai) wrote:
> Hello,
>
> I use Mathematica's MatrixExp to generate the symbolic form of
> a matrix's exponential. It gives me lots of
> I x -I x -I x I x
> E E I E IE
> --- + ------ and -------- - -----
> 2 2 2 2
> which should be converted to Cos[x] and Sin[x], respectively. Does anyone
> know how to do this ?
>
> Thanks a lot!
>
> Yeou-Jyh Tsai
> tsai at relgyro.stanford.edu
You can use the function ComplexToTrig, which is defined in
Algebra`Trigonometry`one of the standard packages distributed
with Mathematica. For example:
In[1]:=
Needs[ "Algebra`Trigonometry`" ]
In[2]:=
ComplexToTrig[ Exp[I x]/2+Exp[-I x]/2 ]
Out[2]=
Cos[x] - I Sin[x] Cos[x] + I Sin[x]
----------------- + -----------------
2 2
In[3]:=
Together[ % ]
Out[3]=
Cos[x]
I hope this helps.
--Ian
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Ian Collier
Wolfram Research, Inc.
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tel:(217)-398-0700 fax:(217)-398-0747 ianc at wolfram.com
Wolfram Research Home Page: http://www.wolfram.com/
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