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). | |
| − | < | + | |
| − | + | {| | |
| − | + | |Cosine | |
| − | + | |Unit Circle on the Complex Plane | |
| − | + | |- | |
| − | + | | <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> | ||
| + | | <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> | ||
| − | + | |} | |
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[[Category:Contributions]] | [[Category:Contributions]] | ||
| + | [[Category:Examples]] | ||
| + | |||
| + | [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 |
