Difference between revisions of "Trigonometric functions"

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The well known trigonometric functions can be visualized on the circle
 +
of radius 1. See [http://en.wikipedia.org/wiki/Trigonometric_functions http://en.wikipedia.org/wiki/Trigonometric_functions] for the definitions.
 +
* '''Tangent''':  <math>\tan x = \frac{\sin x}{\cos x}</math>
 +
* '''Cotangent''': <math>\cot x = \frac{\cos x}{\sin x}</math>
 +
* '''Secant''':    <math>\sec x = \frac{1}{\cos x}</math>
 +
* '''Cosecant''':  <math>\csc x = \frac{1}{\sin x}</math>
 +
 
<jsxgraph width="600" height="600" box="box">
 
<jsxgraph width="600" height="600" box="box">
var brd = JXG.JSXGraph.initBoard('box', {axis:true, originX: 300, originY: 300, grid:true, unitX: 200, unitY: 200, axis:true});
+
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-3, 3, 3, -3]});
 +
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('glider',[0.4,1.0,c],{name:'',withLabel:false});
 +
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',[p0,p2],{straightFirst:false,straightLast:false,strokeColor:'black'});  // Hypotenuse
 +
brd.create('line',[p2,p3],{straightFirst:false,straightLast:false,strokeColor:'red'});    // sin
 +
brd.create('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'});    // cos
 +
 
 +
var t = brd.create('tangent',[p2],{visible:false});
 +
var p5 = brd.create('intersection',[t,ax,0],{visible:false,name:'',withLabel:false});
 +
var p6 = brd.create('intersection',[t,ay,0],{visible:false,name:'',withLabel:false});
 +
brd.create('line',[p5,p6],{straightFirst:false,straightLast:false});                      // tan + cot
 +
brd.create('line',[p0,p6],{straightFirst:false,straightLast:false,strokeColor:'green'});  // csc
 +
brd.create('line',[p0,p5],{straightFirst:false,straightLast:false,strokeColor:'green'});  // sec
 +
 
 +
brd.create('text',[
 +
        function(){return (p0.X()+p2.X())*0.5;},
 +
        function(){return (p0.Y()+p2.Y())*0.5;},
 +
        '1'],{});
 +
 
 +
brd.create('text',[
 +
        function(){return (p2.X()+p4.X())*0.3;},
 +
        function(){return (p2.Y()+p4.Y())*0.5;},
 +
        'cos'],{});
 +
 
 +
brd.create('text',[
 +
        function(){return (p2.X()+p3.X())*0.5;},
 +
        function(){return (p2.Y()+p3.Y())*0.5;},
 +
        'sin'],{});
 +
 
 +
brd.create('text',[
 +
        function(){return 0.1+(p2.X()+p5.X())*0.5;},
 +
        function(){return 0.1+(p2.Y()+p5.Y())*0.5;},
 +
        'tan'],{});
 +
 
 +
brd.create('text',[
 +
        function(){return 0.1+(p2.X()+p6.X())*0.5;},
 +
        function(){return 0.1+(p2.Y()+p6.Y())*0.5;},
 +
        'cot'],{});
 +
 
 +
brd.create('text',[
 +
        function(){return -0.2+(p0.X()+p6.X())*0.5;},
 +
        function(){return (p0.Y()+p6.Y())*0.5;},
 +
        'csc'],{});
 +
 
 +
brd.create('text',[
 +
        function(){return (p0.X()+p5.X())*0.5;},
 +
        function(){return (p0.Y()+p5.Y())*0.5;},
 +
        'sec'],{});
 
</jsxgraph>
 
</jsxgraph>
 +
 +
===The JavaScript Code===
 +
<source lang="javascript">
 +
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-3, 3, 3, -3]});
 +
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('glider',[0.4,1.0,c],{name:'',withLabel:false});
 +
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',[p0,p2],{straightFirst:false,straightLast:false,strokeColor:'black'});  // Hypotenuse
 +
brd.create('line',[p2,p3],{straightFirst:false,straightLast:false,strokeColor:'red'});    // sin
 +
brd.create('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'});    // cos
 +
 +
var t = brd.create('tangent',[p2],{visible:false});
 +
var p5 = brd.create('intersection',[t,ax,0],{visible:false,name:'',withLabel:false});
 +
var p6 = brd.create('intersection',[t,ay,0],{visible:false,name:'',withLabel:false});
 +
brd.create('line',[p5,p6],{straightFirst:false,straightLast:false});                      // tan + cot
 +
brd.create('line',[p0,p6],{straightFirst:false,straightLast:false,strokeColor:'green'});  // csc
 +
brd.create('line',[p0,p5],{straightFirst:false,straightLast:false,strokeColor:'green'});  // sec
 +
 +
brd.create('text',[
 +
        function(){return (p0.X()+p2.X())*0.5;},
 +
        function(){return (p0.Y()+p2.Y())*0.5;},
 +
        '1'],{});
 +
 +
brd.create('text',[
 +
        function(){return (p2.X()+p4.X())*0.3;},
 +
        function(){return (p2.Y()+p4.Y())*0.5;},
 +
        'cos'],{});
 +
 +
brd.create('text',[
 +
        function(){return (p2.X()+p3.X())*0.5;},
 +
        function(){return (p2.Y()+p3.Y())*0.5;},
 +
        'sin'],{});
 +
 +
brd.create('text',[
 +
        function(){return 0.1+(p2.X()+p5.X())*0.5;},
 +
        function(){return 0.1+(p2.Y()+p5.Y())*0.5;},
 +
        'tan'],{});
 +
 +
brd.create('text',[
 +
        function(){return 0.1+(p2.X()+p6.X())*0.5;},
 +
        function(){return 0.1+(p2.Y()+p6.Y())*0.5;},
 +
        'cot'],{});
 +
 +
brd.create('text',[
 +
        function(){return -0.2+(p0.X()+p6.X())*0.5;},
 +
        function(){return (p0.Y()+p6.Y())*0.5;},
 +
        'csc'],{});
 +
 +
brd.create('text',[
 +
        function(){return (p0.X()+p5.X())*0.5;},
 +
        function(){return (p0.Y()+p5.Y())*0.5;},
 +
        'sec'],{});
 +
</source>
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Geometry]]
 
[[Category:Geometry]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Latest revision as of 18:10, 20 February 2013

The well known trigonometric functions can be visualized on the circle of radius 1. See http://en.wikipedia.org/wiki/Trigonometric_functions for the definitions.

  • Tangent: [math]\tan x = \frac{\sin x}{\cos x}[/math]
  • Cotangent: [math]\cot x = \frac{\cos x}{\sin x}[/math]
  • Secant: [math]\sec x = \frac{1}{\cos x}[/math]
  • Cosecant: [math]\csc x = \frac{1}{\sin x}[/math]

The JavaScript Code

var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-3, 3, 3, -3]});
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('glider',[0.4,1.0,c],{name:'',withLabel:false});
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',[p0,p2],{straightFirst:false,straightLast:false,strokeColor:'black'});   // Hypotenuse
brd.create('line',[p2,p3],{straightFirst:false,straightLast:false,strokeColor:'red'});     // sin
brd.create('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'});     // cos

var t = brd.create('tangent',[p2],{visible:false});
var p5 = brd.create('intersection',[t,ax,0],{visible:false,name:'',withLabel:false});
var p6 = brd.create('intersection',[t,ay,0],{visible:false,name:'',withLabel:false});
brd.create('line',[p5,p6],{straightFirst:false,straightLast:false});                       // tan + cot
brd.create('line',[p0,p6],{straightFirst:false,straightLast:false,strokeColor:'green'});   // csc
brd.create('line',[p0,p5],{straightFirst:false,straightLast:false,strokeColor:'green'});   // sec

brd.create('text',[
        function(){return (p0.X()+p2.X())*0.5;},
        function(){return (p0.Y()+p2.Y())*0.5;},
        '1'],{});

brd.create('text',[
        function(){return (p2.X()+p4.X())*0.3;},
        function(){return (p2.Y()+p4.Y())*0.5;},
        'cos'],{});

brd.create('text',[
        function(){return (p2.X()+p3.X())*0.5;},
        function(){return (p2.Y()+p3.Y())*0.5;},
        'sin'],{});

brd.create('text',[
        function(){return 0.1+(p2.X()+p5.X())*0.5;},
        function(){return 0.1+(p2.Y()+p5.Y())*0.5;},
        'tan'],{});

brd.create('text',[
        function(){return 0.1+(p2.X()+p6.X())*0.5;},
        function(){return 0.1+(p2.Y()+p6.Y())*0.5;},
        'cot'],{});

brd.create('text',[
        function(){return -0.2+(p0.X()+p6.X())*0.5;},
        function(){return (p0.Y()+p6.Y())*0.5;},
        'csc'],{});

brd.create('text',[
        function(){return (p0.X()+p5.X())*0.5;},
        function(){return (p0.Y()+p5.Y())*0.5;},
        'sec'],{});