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I have a plot but the x and y axis need to be switched. The problem is that I can't explicitly solve for the other so I can change the axis.

e = .65;

Ec[M_] = M + 
  Sum[(1/2^(n - 1)*
      Sum[((-1)^k*(n - 2*k)^(n - 1))/((n - k)!*k!)*
        Sin[(n - 2*k)*M], {k, 0, Floor[n/2]}])*e^n, {n, 1, 3}]
Plot[Ec[M], {M, 0, 2 \[Pi]}, 
 PlotRange -> {{0, 2 \[Pi]}, {0, 2 \[Pi]}}]

Basically, I want Ec to be on the x axis and M the y axis. As of right now, they are swapped.

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  • $\begingroup$ You've seen ParametricPlot[]? $\endgroup$ – J. M. will be back soon May 27 '13 at 3:35
  • $\begingroup$ @J.M. I have used it before. $\endgroup$ – dustin May 27 '13 at 3:35
  • 1
    $\begingroup$ In that case, ponder on what ParametricPlot[{Sin[y], y}, {y, 0, 3}] does, and see if you can apply this to your problem at hand. $\endgroup$ – J. M. will be back soon May 27 '13 at 3:38
  • 2
    $\begingroup$ I was actually encouraging you to answer your own question using my hint... ;) Please do so. $\endgroup$ – J. M. will be back soon May 27 '13 at 3:42
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Per J.M.s suggestion, the solution to the problem is:

e = .65;

Ec[M_] = M + 
   Sum[(1/2^(n - 1)*
       Sum[((-1)^k*(n - 2*k)^(n - 1))/((n - k)!*k!)*
         Sin[(n - 2*k)*M], {k, 0, Floor[n/2]}])*e^n, {n, 1, 10}];
ParametricPlot[{Ec[M], M}, {M, 0, 2 \[Pi]}, 
 PlotRange -> {{0, 2 \[Pi]}, {0, 2 \[Pi]}}, GridLines -> Automatic, 
 PlotStyle -> Red]
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  • $\begingroup$ Excellent. ${}$ $\endgroup$ – J. M. will be back soon May 27 '13 at 3:50
  • $\begingroup$ @MichaelE2 not for another day. $\endgroup$ – dustin May 27 '13 at 23:31
  • $\begingroup$ OK - just wanted to make sure you knew. Sorry to be a bother. $\endgroup$ – Michael E2 May 28 '13 at 0:46

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