Groups > comp.soft-sys.math.mathematica > #16861

Inverse function solution

From	Narasimham <mathma18@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Inverse function solution
Date	2014-04-28 01:45 +0000
Message-ID	<ljkbqu$1u1$1@smc.vnet.net> (permalink)
Organization	Time-Warner Telecom

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Solve[ {x == Cos[u], y == Cos[u + v] }, {u, v} ] 

Its closed/analytic solution is not possible, even numerically. 

The known solutions are ellipses from sine waves with a phase difference, having x^2, x y and y^2 terms, as also sketched in Lissajous curves: 

ParametricPlot[{Cos[u], Cos[u + v]}, {u, -Pi, Pi}, {v, -Pi, Pi}] 

Can there be a work around? 

Narasimham

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Inverse function solution Narasimham <mathma18@gmail.com> - 2014-04-28 01:45 +0000
  Re: Inverse function solution Roland Franzius <roland.franzius@uos.de> - 2014-04-29 05:32 +0000

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