Difference between revisions of "Cosine"

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Geometrically, the cosine is a projection of the complex number exp(−ix) to the real axis. The behavior of the cosine function can be studied in the following interactive figure, where you can drag the point x and observe the behaviour of the complex number exp(−ix) and the value of cosine(x).  
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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).  
  <jsxgraph box="boxR" width="500" height="500">  
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{|
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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">  
  <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);
 
       brd1.addChild(brd);
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   </jsxgraph>  
 
   </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