Difference between revisions of "Cosine"

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<html>
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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).
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<link rel="stylesheet" type="text/css" href="http://cpge.livet.free.fr/Ats/squelettes/jsxgraph.css" />
 
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<script type="text/javascript" src="http://cpge.livet.free.fr/Ats/squelettes/jsxgraphcore.js"></script>
 
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<style type="text/css">
 
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  #rot, #rot0, #rot1, #rot2, #rot3, #rot4 {
 
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    -webkit-transform: rotate(90deg);
 
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    -moz-transform: rotate(90deg);
 
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    -o-transform: rotate(90deg);
 
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    filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=1);
 
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  }
 
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</style>
 
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<body>
 
  
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<table>
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{|
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<tr>
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|Cosine
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<td>Complex Plane</td><td>Cosine Graph</td>
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|Unit Circle on the Complex Plane
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</tr>
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|-
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<tr>
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|  <jsxgraph box="boxR" width="500" height="500">
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<td><div id="box" class="jxgbox" style="width:500px; height:500px;"></div></td>
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      var brd1 = JXG.JSXGraph.initBoard('boxR', {boundingbox: [-10, 1.5, 10, -1.5], axis:true});
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<td><div id="boxR" class="jxgbox" style="width:500px; height:500px;"></div></td>
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      var xr = brd1.create('line',[[-9,0],[9,0]],{visible:false});
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</tr>
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      var x = brd1.create('glider',[-9,0,xr],{visible:true, name:'x'});
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</table>
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      var y = brd1.create('point',[x.X(),Math.cos(x.X())],{size:1,name:'',strokeColor:'green'});
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      var x1 = brd1.create('segment',[x,y],{visible:true, straightFirst:false,straightLast:false,strokeColor:'red'});
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      x.on('drag', function(){ transform(x);});
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      var f = brd1.create('functiongraph',
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          [function(x){
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    return Math.cos(x);  
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          }]);
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      brd1.create('text',[
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        function(){return x.X()+0.3;},
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        function(){return y.Y()*0.5;},
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        'cos'],{});
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      function transform(x) {
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        p2.setPosition(JXG.COORDS_BY_USER,[Math.cos(x.X()),Math.sin(x.X())]);
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        y.setPosition(JXG.COORDS_BY_USER,[x.X(),Math.cos(x.X())]);
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        brd.update();
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      }
  
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<script language="javascript" type="text/javascript">
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  </jsxgraph>
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|  <jsxgraph box="box" width="500" height="500">  
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var brd1 = JXG.JSXGraph.initBoard('boxR', {boundingbox: [-10, 1.5, 10, -1.5], axis:true});
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      var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-1.5, 1.5, 1.5, -1.5], axis:true});  
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var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-1.5, 1.5, 1.5, -1.5], axis:true});
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      brd1.addChild(brd);
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      var ax = brd.create('line',[[0,0],[1,0]],{visible:false});
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var xr = brd1.create('line',[[-9,0],[9,0]],{visible:false});
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      var ay = brd.create('line',[[0,0],[0,1]],{visible:false});
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var x = brd1.create('glider',[-9,0,xr],{visible:true, name:'x'});
 
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var y = brd1.create('point',[x.X(),Math.cos(x.X())],{size:1,name:'',strokeColor:'green'});
 
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console.log("test1");
 
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var x1 = brd1.create('segment',[x,y],{visible:true, straightFirst:false,straightLast:false,strokeColor:'red'});
 
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x.on('drag', function(){ transform(x);});
 
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var f = brd1.create('functiongraph',[function(x){
 
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return Math.cos(x);
 
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}]);
 
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var ax = brd.create('line',[[0,0],[1,0]],{visible:false});
 
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var ay = brd.create('line',[[0,0],[0,1]],{visible:false});
 
 
   
 
   
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var p0 = brd.create('point',[0,0],{fixed:true,visible:false});
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      var p0 = brd.create('point',[0,0],{fixed:true,visible:false});
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var p1 = brd.create('point',[1,0],{name:'',visible:false,fixed:true});
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      var p1 = brd.create('point',[1,0],{name:'',visible:false,fixed:true});
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var c = brd.create('circle',[p0,p1],{dash:2,strokeWidth:1,strokeOpacity:0.6});
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      var c = brd.create('circle',[p0,p1],{dash:2,strokeWidth:1,strokeOpacity:0.6});
  
  
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var p2 = brd.create('point',[Math.cos(x.X()),Math.sin(x.X())],{name:'exp(ix)',fixed:true,size:1, strokeColor:'green'});
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      var p2 = brd.create('point',[Math.cos(x.X()),Math.sin(x.X())],{name:'exp(ix)',fixed:true,size:1, strokeColor:'green'});
  
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var p3 = brd.create('point',[function(){return p2.X();},0.0],{visible:false,name:'',withLabel:false});
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      var p3 = brd.create('point',[function(){return p2.X();},0.0],{visible:false,name:'',withLabel:false});
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var p4 = brd.create('point',[0.0,function(){return p2.Y();}],{visible:false,name:'',withLabel:false});
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      var p4 = brd.create('point',[0.0,function(){return p2.Y();}],{visible:false,name:'',withLabel:false});
 
   
 
   
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brd.create('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'});    // cos
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      brd.create('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'});    // cos
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brd.create('text',[
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      brd.create('text',[
 
         function(){return (p2.X()+p4.X())*0.3;},
 
         function(){return (p2.X()+p4.X())*0.3;},
 
         function(){return p2.Y()+0.05;},
 
         function(){return p2.Y()+0.05;},
 
         'cos'],{});
 
         'cos'],{});
  
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brd1.create('text',[
 
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        function(){return x.X()+0.3;},
 
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        function(){return y.Y()*0.5;},
 
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        'cos'],{});
 
  
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function transform(x) {
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p2.setPosition(JXG.COORDS_BY_USER,[Math.cos(x.X()),Math.sin(x.X())]);
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  </jsxgraph>
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y.setPosition(JXG.COORDS_BY_USER,[x.X(),Math.cos(x.X())]);
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|}
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brd.update();
 
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}
 
  
  
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</script>
 
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</body>
 
  
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</html>
 
 
[[Category:Contributions]]
 
[[Category:Contributions]]
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[[Category:Examples]]
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 +
[http://www.bookofproofs.org/branches/cosine/ read more about cosine on Bookofproofs]

Latest revision as of 14:21, 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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