# Switching the axis of a plot [duplicate]

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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## marked as duplicate by m_goldberg, Artes, Michael E2, Yves Klett, Oleksandr R.May 27 '13 at 15:38

You've seen ParametricPlot[]? – J. M. May 27 '13 at 3:35
@J.M. I have used it before. – dustin May 27 '13 at 3:35
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. – J. M. May 27 '13 at 3:38
@J.M. thanks, can you post this an answer so I can accept it? – dustin May 27 '13 at 3:40
I was actually encouraging you to answer your own question using my hint... ;) Please do so. – J. M. May 27 '13 at 3:42

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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Excellent. ${}$ – J. M. May 27 '13 at 3:50
@MichaelE2 not for another day. – dustin May 27 '13 at 23:31
OK - just wanted to make sure you knew. Sorry to be a bother. – Michael E2 May 28 '13 at 0:46