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Inverse function solution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132646] Inverse function solution
  • From: Narasimham <mathma18 at gmail.com>
  • Date: Sun, 27 Apr 2014 21:44:44 -0400 (EDT)
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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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