Hi Peter,

I think the resolution in both images is the same, but the rotated image contains necessarily more pixels:

In[10]:= ImageDimensions /@ {img0, img1}
(*  Out[10]= {{500, 300}, {547, 392}}  *)

But as a matter of fact Ottos solution is much more elegant! One just has to make sure that in both plots the same options are used:

pArgs = Sequence[{x, -2*\[Pi], 2*\[Pi]}, PlotRange -> {-3, 3}, ImageSize -> 500];
Plot[x, Evaluate @ pArgs, PlotStyle -> {Opacity[0]}, 
 Epilog -> Inset[Rotate[Plot[Cos[x], Evaluate @ pArgs], -10 Degree]]]

Regards -- Henrik

Hi Henrik and Otto

Thank you very much. I like both of your solutions.

@Henrik: If I copy-paste your code I get following error message: The number of channels must be equal or one of them must be a single-channel image and the other a multichannel image.

The problem is related to the last function ImageMultiply. Any ideas what this means and how I can fix that? I am using Mathematica 10.0.

@Otto: I would like to increase the size of the inset but for some reason this doesn't work. I want both coordinate systems with similar frame size (like in Henriks solution). At the moment the inset is much too small for my taste :-)

I tried several options but I failed.

   Plot[0, {x, -6, 6},
    PlotRange -> {{-2, 2}, {-2, 2}},
    Frame -> True,
    PlotStyle -> Black,
    ImageSize -> 800,
    Epilog -> 
     Inset[Rotate[Plot[Cos[x], {x, -2*\[Pi], 2*\[Pi]}], 30 Degree], {0, 
       0}, {0, 0}, 15]
    ]

Thank you very much for your help,

Peter

Hello Peter,

This will display the rotated plot:

Rotate[Plot[Cos[x], {x, -2*\[Pi], 2*\[Pi]}], 30 Degree]

However, you only get the rotated axes, not the straight ones. You can put it inside another plot, just to get straight axes:

Plot[0, {x, 0, 1}, PlotRange -> {{-2*\[Pi], 2*\[Pi]}, {-3, 3}}, 
 Epilog -> 
  Inset[Rotate[Plot[Cos[x], {x, -2*\[Pi], 2*\[Pi]}], 30 Degree]]]

You can play with the ranges and the size of the Inset to get things right. I cannot say I like the idea of using an additional call to Plot just to generate axes, but I am not being able to display the output of Rotate with Graphics, even if I first evaluate FullGraphics on it. If you could display it with Graphics, then you could display the straight axes and even a frame, if desired.

You may want to see:

http://mathematica.stackexchange.com/questions/80505/how-to-plot-functions-in-multiple-coordinate-systems

and

http://mathematica.stackexchange.com/questions/1003/is-there-an-equivalent-of-fullgraphics-for-graphics3d

OL.

Hi

thank you Otto for your answer. This is only partially what I am looking for. The code that you gave me shows a cos-function rotated by an angle. Now I would like to have a second coordinate system on top of this plot which is rotated by the same angle. Just like in the picture I included in my first post. That is the big challenge for me.

Best regards,

Peter