Re: solving trignometric equ for non trivial solutions
- From: roberson@xxxxxxxxxxxxxxxxxx (Walter Roberson)
- Date: Fri, 1 Feb 2008 19:06:35 +0000 (UTC)
In article <19702142.1201890396398.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
reddy <sujeeth@xxxxxxxxxxxxx> wrote:
here i want to find x interms of k...any general solution??
No. The general solution, according to maple, is
RootOf(cos(_Z)*(exp(_Z))^2+cos(_Z)-2*exp(_Z)) / k
The numerator is independant of k, so if you know the solutions
for one non-zero k, scale them by k to get the general solution.
The cos(_Z) can be grouped,
RootOf(cos(_Z)*(1 + exp(2*_Z)) - 2*exp(_Z)) / k
Since exp(2*_Z) > 2*exp(_Z), the cos(_Z) term ensures that the
expression will flip sign infinitely often with increasing _Z
so there will be infinite number of roots spaced at most Pi apart.
The - 2*exp(_Z) term will, it seems to me, essentially apply an
increasing phase change as you go.
--
"Is there any thing whereof it may be said, See, this is new? It hath
been already of old time, which was before us." -- Ecclesiastes
.
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