Difference between revisions of "Cosine"
From JSXGraph Wiki
Jump to navigationJump to searchBookofproofs (talk | contribs) |
Bookofproofs (talk | contribs) |
||
(8 intermediate revisions by the same user not shown) | |||
Line 1: | Line 1: | ||
− | + | 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}); | ||
Line 33: | Line 52: | ||
</jsxgraph> | </jsxgraph> | ||
− | + | |} | |
− | + | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
[[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 |