Re: symbolic solution (ArcTan)
- To: mathgroup at smc.vnet.net
- Subject: [mg33302] Re: [mg33289] symbolic solution (ArcTan)
- From: Andrzej Kozlowski <andrzej at lineone.net>
- Date: Thu, 14 Mar 2002 02:22:06 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
In the sense that you probably have in mind, what you are asking for is
not just impossible but meaningless. This equation is non-algebraic so
there is no "symbolic way" to express its (single) root. But in another
sense it is very easy. Just give the root of this equation a name, say
P and then do something like this:
In[1]:=
NumericQ[P]=True;
In[2]:=
N[P,m_:16]:=
Block[{x},
x/.FindRoot[x==ArcTan[5-Pi+x],{x,1},WorkingPrecision->m]]
You can now compute the numerical value of P to an arbitrary precision:
In[3]:=
N[P,100]
Out[3]=
1.2605291621674156311141830999192315723940257255633201262021666467377750400719\
00640976962651518036469
Now you have, (for what it's worth), a "symbolic solution" to your
equation, namely P.
On Wednesday, March 13, 2002, at 09:15 AM, Paul wrote:
> Is it possible to find an exact symbolic solution for x in ( x ==
> ArcTan[5 - Pi + x] )?
>
> I know that ( FindRoot[x == ArcTan[5 - Pi + x], {x, 1}] ) yields a
> numeric solution ~= 1.2605, but again, I'd like to find an exact
> symbolic solution if possible.
>
> Paul
>
>
>
>
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/