title: Wrong graph when trying to rotate coordinates
body: <p>Consider the following toy data:</p>
  
  <pre><code>clear
  input double x1 float y1
                     0         0
  .0013440860215053765 .02503477
  .0013440860215053765 .05006954
   .005376344086021506  .0751043
   .009408602150537635 .10013908
    .01747311827956989 .12482615
    .03225806451612903  .1498609
   .056451612903225805  .1748957
    .07661290322580645 .19993046
    .09946236559139784 .22496523
    .15725806451612903       .25
     .2110215053763441  .2750348
    .32661290322580644  .3000695
     .3803763440860215  .3251043
     .4986559139784946  .3497914
      .603494623655914  .3748261
      .706989247311828  .3998609
     .7661290322580645  .4248957
     .8064516129032258  .4499305
      .885752688172043  .4749652
     .9099462365591398        .5
                     1  .5250348
     .9811827956989247  .5500696
     .8870967741935484  .5751043
     .7661290322580645  .5997913
     .6599462365591398  .6248261
     .5873655913978495  .6498609
     .5282258064516129  .6748957
    .40053763440860213  .6999304
     .3279569892473118  .7249652
     .2163978494623656       .75
    .15053763440860216  .7750348
    .09408602150537634  .8000696
    .06586021505376344  .8247566
    .04973118279569892  .8497913
   .024193548387096774  .8748261
   .025537634408602152  .8998609
   .006720430107526882  .9248957
   .002688172043010753  .9499304
   .004032258064516129  .9749652
                     0         1
  end
  
  twoway scatter y1 x1
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/cV5yU.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/cV5yU.jpg" alt="enter image description here"></a></p>
  
  <p>When I try to rotate the entire graph by say <code>20</code> degrees <em>counter</em>-clockwise:</p>
  
  <pre><code>local theta = 0.349066
  
  generate x2 = (x1 * cos(`theta') ) - (y1 * sin(`theta') )  
  generate y2 = (x1 * sin(`theta') ) - (y1 * cos(`theta') ) 
  </code></pre>
  
  <p>The coordinates transform as follows:</p>
  
  <pre><code>clear
  input float(x2 y2)
            0           0
  -.007299372 -.023065284
   -.01586177  -.04659027
  -.020635087  -.06873614
  -.025408404  -.09088202
  -.026273714  -.11132205
   -.02094281  -.12979028
  -.006770712  -.14504059
  .0036123034     -.16167
   .016521374     -.17738
    .06226916   -.1811377
    .10422786   -.1862745
    .20428585   -.1702649
    .24624455   -.1754017
     .3489475   -.1581459
     .4389013  -.14581393
      .527592  -.13394167
    .57460284  -.13723963
     .6039312   -.1469735
     .6698875   -.1433759
     .6840596   -.1586262
       .76012    -.151351
     .7338752  -.18131188
     .6369009  -.23701614
    .51478493   -.3015878
     .4064434   -.3614295
     .3296775   -.4097785
    .26554185  -.45353055
    .13699183  -.52072746
    .06022594   -.5690765
   -.05316776    -.630757
   -.12361852   -.6768075
    -.1852281   -.7196401
   -.22019514   -.7524921
   -.24391386   -.7815335
    -.2764738   -.8137929
   -.28377315   -.8368582
    -.3100179   -.8668191
    -.3223694   -.8917232
    -.3296688   -.9147884
    -.3420203   -.9396926
  end
  </code></pre>
  
  <p></p>
  
  <pre><code>twoway scatter y2 x2
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/Bx8DV.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Bx8DV.jpg" alt="enter image description here"></a></p>
  
  <p>What am I missing? </p>
  
  <p>Note that I have also tried to center the values first around a specific point.</p>
  
  <p>In addition, I would also like the solution to account for different axes scales and graph aspect ratio.</p>
  
  <p>For example:</p>
  
  <pre><code>clear
  input float y double x
  -2013                 .001
  -1941 .0010053763440860215
  -1869 .0010053763440860215
  -1797 .0010215053763440861
  -1725 .0010376344086021505
  -1654 .0010698924731182796
  -1582 .0011290322580645162
  -1510 .0012258064516129032
  -1438 .0013064516129032257
  -1366 .0013978494623655914
  -1294 .0016290322580645162
  -1222 .0018440860215053765
  -1150 .0023064516129032257
  -1078 .0025215053763440864
  -1007 .0029946236559139786
   -935  .003413978494623656
   -863  .003827956989247312
   -791  .004064516129032258
   -719  .004225806451612904
   -647  .004543010752688172
   -575  .004639784946236559
   -503                 .005
   -431 .0049247311827956995
   -359  .004548387096774194
   -288  .004064516129032258
   -216 .0036397849462365592
   -144  .003349462365591398
    -72 .0031129032258064514
      0 .0026021505376344085
     72  .002311827956989247
    144 .0018655913978494624
    216 .0016021505376344087
    288 .0013763440860215053
    359 .0012634408602150537
    431 .0011989247311827958
    503 .0010967741935483872
    575 .0011021505376344087
    647 .0010268817204301076
    719  .001010752688172043
    791 .0010161290322580644
    863                 .001
  end
  
  twoway scatter y x
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/23TdK.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/23TdK.jpg" alt="enter image description here"></a></p>
  
  <p>The <code>y-xis</code> of this graph is <code>4</code> inches while the <code>x-axis</code> is <code>5.5</code> inches (aspect ratio of <code>1.375</code>).</p>
  
  <p>I have consulted a number of posts including the following:</p>
  
  <ul>
  <li><p><a href="https://stackoverflow.com/questions/45648779/programmatically-rotate-shapes-using-coordinates">Programmatically rotate shapes using coordinates</a></p></li>
  <li><p><a href="https://stackoverflow.com/questions/9190149/how-to-rotate-coordinate-system">How to rotate coordinate system?</a></p></li>
  </ul>
  
  <p>I hope what I am trying to do is clear but I will be happy to clarify further.</p>