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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

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

**Follow-Ups**:**Re: Inverse function solution***From:*Murray Eisenberg <murray@math.umass.edu>

**Re: Inverse function solution***From:*Bob Hanlon <hanlonr357@gmail.com>