Cosine: Difference between revisions
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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 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}); | ||
| Line 23: | Line 27: | ||
</jsxgraph> | </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}); | |||
brd1.addChild(brd); | |||
var ax = brd.create('line',[[0,0],[1,0]],{visible:false}); | |||
var ay = brd.create('line',[[0,0],[0,1]],{visible:false}); | |||
var p0 = brd.create('point',[0,0],{fixed:true,visible:false}); | |||
var p1 = brd.create('point',[1,0],{name:'',visible:false,fixed:true}); | |||
var c = brd.create('circle',[p0,p1],{dash:2,strokeWidth:1,strokeOpacity:0.6}); | |||
var p2 = brd.create('point',[Math.cos(x.X()),Math.sin(x.X())],{name:'exp(ix)',fixed:true,size:1, strokeColor:'green'}); | |||
var p3 = brd.create('point',[function(){return p2.X();},0.0],{visible:false,name:'',withLabel:false}); | |||
var p4 = brd.create('point',[0.0,function(){return p2.Y();}],{visible:false,name:'',withLabel:false}); | |||
brd.create('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'}); // cos | |||
brd.create('text',[ | |||
function(){return (p2.X()+p4.X())*0.3;}, | |||
function(){return p2.Y()+0.05;}, | |||
'cos'],{}); | |||
</jsxgraph> | |||
|} | |||
[[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 |
