Difference between revisions of "Cosine"

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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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{|
  <jsxgraph box="boxR" width="500" height="500">  
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|Cosine
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|Unit Circle on the Complex Plane
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|-
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<jsxgraph box="boxR" width="500" height="500">  
 
       var brd1 = JXG.JSXGraph.initBoard('boxR', {boundingbox: [-10, 1.5, 10, -1.5], axis:true});
 
       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 xr = brd1.create('line',[[-9,0],[9,0]],{visible:false});
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   </jsxgraph>  
 
   </jsxgraph>  
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|  <jsxgraph box="box" width="500" height="500">
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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 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 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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 +
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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 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('text',[
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        function(){return (p2.X()+p4.X())*0.3;},
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        function(){return p2.Y()+0.05;},
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        'cos'],{});
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 +
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  </jsxgraph>
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|}
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 +
  
 
[[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 15:21, 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