# Re: 1+Cos[x]Cosh[x]==0 ?

• To: mathgroup@smc.vnet.net
• Subject: [mg12124] Re: 1+Cos[x]Cosh[x]==0 ?
• From: "Stephen P Luttrell" <luttrell@signal.dra.hmg.gb>
• Date: Mon, 27 Apr 1998 01:46:09 -0400
• Organization: Defence Evaluation and Research Agency
• References: <6hpgug\$djf@smc.vnet.net>

```>
>How to solve "1 + Cos[x] Cosh[x] == 0"?  I will probably need just the
>first five, positive solution of "x".
>

First of all plot out the left hand side in such a way that it is easy
to estimate good starting points for each of the roots.

The following input will do this for you

Plot[Log[Abs[1 + Cos[x] Cosh[x]]] ,{x,0,15}]

Select the plot, hold down CTRL (or whatever equivalent modifier key
your system happens to use), and move the cursor around to read off the
approximate coordinates of each root, and use these to construct the
starting points in the following expression

Map[FindRoot[1 + Cos[x] Cosh[x]==0,{x,#}]&,{1.78,4.64,7.74,11.0,14.1}]

which evaluates to yield the output

{{x -> 1.8751}, {x -> 4.69409}, {x -> 7.85476}, {x -> 10.9955}, {x ->
14.1372}}

====================================================

Stephen P Luttrell
luttrell@signal.dra.hmg.gb
Room EX21, DERA                                    01684-894384 (fax)
Malvern, Worcs, WR14 3PS, U.K.
http://www.dra.hmg.gb/cis5pip/Welcome.html

```

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