Cosine: Difference between revisions

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<html>
The cosine is a projection of the complex number exp(−ix) (which is a point on the unit circle in the complex plane) to the real axis on the complex plane. In the following interactive figure, you can drag the point x on the real axis and observe the behaviour of the complex number exp(−ix) and the varying value of cosine(x).
  <link rel="stylesheet" type="text/css" href="http://cpge.livet.free.fr/Ats/squelettes/jsxgraph.css" />
 
<script type="text/javascript" src="http://cpge.livet.free.fr/Ats/squelettes/jsxgraphcore.js"></script>
{|
<body>
|Cosine
<table>
|Unit Circle on the Complex Plane
<tr>
|-
<td>Complex Plane</td><td>Cosine Graph</td>
| <jsxgraph box="boxR" width="500" height="500">
</tr>
      var brd1 = JXG.JSXGraph.initBoard('boxR', {boundingbox: [-10, 1.5, 10, -1.5], axis:true});
<tr>
      var xr = brd1.create('line',[[-9,0],[9,0]],{visible:false});
<td>
      var x = brd1.create('glider',[-9,0,xr],{visible:true, name:'x'});
  <jsxgraph box="box" width="500" height="500">  
      var y = brd1.create('point',[x.X(),Math.cos(x.X())],{size:1,name:'',strokeColor:'green'});
      var x1 = brd1.create('segment',[x,y],{visible:true, straightFirst:false,straightLast:false,strokeColor:'red'});
      x.on('drag', function(){ transform(x);});
      var f = brd1.create('functiongraph',
          [function(x){
    return Math.cos(x);
          }]);
      brd1.create('text',[
        function(){return x.X()+0.3;},
        function(){return y.Y()*0.5;},
        'cos'],{});
      function transform(x) {
        p2.setPosition(JXG.COORDS_BY_USER,[Math.cos(x.X()),Math.sin(x.X())]);
        y.setPosition(JXG.COORDS_BY_USER,[x.X(),Math.cos(x.X())]);
        brd.update();
      }
 
  </jsxgraph>  
|  <jsxgraph box="box" width="500" height="500">  
       var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-1.5, 1.5, 1.5, -1.5], axis:true});  
       var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-1.5, 1.5, 1.5, -1.5], axis:true});  
      brd1.addChild(brd);
       var ax = brd.create('line',[[0,0],[1,0]],{visible:false});
       var ax = brd.create('line',[[0,0],[1,0]],{visible:false});
       var ay = brd.create('line',[[0,0],[0,1]],{visible:false});
       var ay = brd.create('line',[[0,0],[0,1]],{visible:false});
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   </jsxgraph>  
   </jsxgraph>  
</td>
|}
<td>
 
  <jsxgraph box="boxR" width="500" height="500">
      var brd1 = JXG.JSXGraph.initBoard('boxR', {boundingbox: [-10, 1.5, 10, -1.5], axis:true});
      var xr = brd1.create('line',[[-9,0],[9,0]],{visible:false});
      var x = brd1.create('glider',[-9,0,xr],{visible:true, name:'x'});
      var y = brd1.create('point',[x.X(),Math.cos(x.X())],{size:1,name:'',strokeColor:'green'});
      var x1 = brd1.create('segment',[x,y],{visible:true, straightFirst:false,straightLast:false,strokeColor:'red'});
      x.on('drag', function(){ transform(x);});
      var f = brd1.create('functiongraph',
          [function(x){
    return Math.cos(x);
          }]);
      brd1.create('text',[
        function(){return x.X()+0.3;},
        function(){return y.Y()*0.5;},
        'cos'],{});
      function transform(x) {
        p2.setPosition(JXG.COORDS_BY_USER,[Math.cos(x.X()),Math.sin(x.X())]);
        y.setPosition(JXG.COORDS_BY_USER,[x.X(),Math.cos(x.X())]);
        brd.update();
      }


  </jsxgraph>
</td>
</tr>
</table>
</body>


</html>
[[Category:Contributions]]
[[Category:Contributions]]
[[Category:Examples]]
[http://www.bookofproofs.org/branches/cosine/ read more about cosine on Bookofproofs]

Latest revision as of 13:21, 6 March 2016

The cosine is a projection of the complex number exp(−ix) (which is a point on the unit circle in the complex plane) to the real axis on the complex plane. In the following interactive figure, you can drag the point x on the real axis and observe the behaviour of the complex number exp(−ix) and the varying value of cosine(x).

Cosine Unit Circle on the Complex Plane

read more about cosine on Bookofproofs

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