1+Cos[x]Cosh[x]==0 ?

Eddy Wibowo

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Apr 24, 1998, 3:00:00 AM4/24/98

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Hi everybody,

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

Many thanks before hand.

-Eddy

SiposG

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Apr 26, 1998, 3:00:00 AM4/26/98

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>How to solve "1 + Cos[x] Cosh[x] == 0"?

Does this help?
Solve[TrigToExp[ Cos[x] Cosh[x]==0 ],x]

George

Stephen P Luttrell

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Apr 26, 1998, 3:00:00 AM4/26/98

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>
>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}}

which solves your problem.

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

Stephen P Luttrell
lutt...@signal.dra.hmg.gb
Adaptive Systems Theory 01684-894046 (phone)
Room EX21, DERA 01684-894384 (fax)
Malvern, Worcs, WR14 3PS, U.K.
http://www.dra.hmg.gb/cis5pip/Welcome.html

Bob Hanlon

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Apr 26, 1998, 3:00:00 AM4/26/98

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Plot[1 + Cos[x]*Cosh[x], {x, 0, 3}];

FindRoot[1 + Cos[x]*Cosh[x] == 0, {x, 1.9}]

{x -> 1.875104213439618}

Plot[1 + Cos[x]*Cosh[x], {x, 3, 5}];

FindRoot[1 + Cos[x]*Cosh[x] == 0, {x, 4.7}]

{x -> 4.694091134241512}

Plot[1 + Cos[x]*Cosh[x], {x, 5, 8}];

FindRoot[1 + Cos[x]*Cosh[x] == 0, {x, 7.8}]

{x -> 7.854757438345366}

Plot[1 + Cos[x]*Cosh[x], {x, 8, 11}];

FindRoot[1 + Cos[x]*Cosh[x] == 0, {x, 11.}]

{x -> 10.99554073487546}

Plot[1 + Cos[x]*Cosh[x], {x, 11, 15}];

FindRoot[1 + Cos[x]*Cosh[x] == 0, {x, 14.2}]

{x -> 14.13716839104647}

Bob Hanlon

Bruce Wolk

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Apr 26, 1998, 3:00:00 AM4/26/98

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On 24 Apr 1998 04:02:24 -0400, Eddy Wibowo <ew4...@bristol.ac.uk> wrote:

>Hi everybody,

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

>Many thanks before hand.
>
>-Eddy
>
>

How about

In[1]:=
Table[x/.FindRoot[1+Cos[x] Cosh[x]==0,{x,i}],{i,1.5,5 Pi,Pi}] Out[1]=
{1.8751,4.69409,7.85476,10.9955,14.1372}

I guessed 1.5 to start and then figured I would get a root every Pi or
so.

Cheers,

Bruce

Sherman.Reed

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Apr 28, 1998, 3:00:00 AM4/28/98

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Eddy,
I plotted the equation 1+(Cos[x])*(Cosh[x]) to get approx values of the
roots. I found xapprox to be {2,4.5,8,11,14,17}.

I then used FindRoot[1+(Cos[x])*(Cosh[x]) ==0,{x,xapprox}] to get good
values of the root.

Sherman C. Reed
sherma...@worldnet.att.net
----------
> From: Eddy Wibowo <ew4...@bristol.ac.uk>
> To: math...@smc.vnet.net
> Subject: [mg12109] 1+Cos[x]Cosh[x]==0 ?
> Date: Saturday, April 25, 1998 12:30 AM

Michael Milirud

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May 1, 1998, 3:00:00 AM5/1/98

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Eddy Wibowo wrote in message <6hpgug$d...@smc.vnet.net>...

>Hi everybody,
>
>How to solve "1 + Cos[x] Cosh[x] == 0"? I will probably need just the
>first five, positive solution of "x".
>
>Many thanks before hand.
>
>-Eddy

Got for Plot[1+Cos[x]Cosh[x],{x,0,5}] You will see the first two roots.
Use the FindRoot[1+Cos[x]Cosh[x]==0,x->2] and then x->5.
Do the same for the next range 4,8 and so on. The function behaves like
crazy for big +-x-es and you can see that if you plot (-100,100) on
(-1000,1000) it is just a black block ;)

Michael