Difference between revisions of "Trigonometric functions"

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Line 8: Line 8:
 
<jsxgraph width="600" height="600" box="box">
 
<jsxgraph width="600" height="600" box="box">
 
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-3, 3, 3, -3]});
 
var brd = JXG.JSXGraph.initBoard('box', {boundingbox: [-3, 3, 3, -3]});
var ax = brd.createElement('line',[[0,0],[1,0]],{visible:false});
+
var ax = brd.create('line',[[0,0],[1,0]],{visible:false});
var ay = brd.createElement('line',[[0,0],[0,1]],{visible:false});
+
var ay = brd.create('line',[[0,0],[0,1]],{visible:false});
  
var p0 = brd.createElement('point',[0,0],{fixed:true,visible:false});
+
var p0 = brd.create('point',[0,0],{fixed:true,visible:false});
var p1 = brd.createElement('point',[1,0],{name:'',visible:false,fixed:true});
+
var p1 = brd.create('point',[1,0],{name:'',visible:false,fixed:true});
var c = brd.createElement('circle',[p0,p1],{dash:2,strokeWidth:1,strokeOpacity:0.6});
+
var c = brd.create('circle',[p0,p1],{dash:2,strokeWidth:1,strokeOpacity:0.6});
var p2 = brd.createElement('glider',[0.4,1.0,c],{name:'',withLabel:false});
+
var p2 = brd.create('glider',[0.4,1.0,c],{name:'',withLabel:false});
var p3 = brd.createElement('point',[function(){return p2.X();},0.0],{visible:false,name:'',withLabel:false});
+
var p3 = brd.create('point',[function(){return p2.X();},0.0],{visible:false,name:'',withLabel:false});
var p4 = brd.createElement('point',[0.0,function(){return p2.Y();}],{visible:false,name:'',withLabel:false});
+
var p4 = brd.create('point',[0.0,function(){return p2.Y();}],{visible:false,name:'',withLabel:false});
  
brd.createElement('line',[p0,p2],{straightFirst:false,straightLast:false,strokeColor:'black'});  // Hypotenuse
+
brd.create('line',[p0,p2],{straightFirst:false,straightLast:false,strokeColor:'black'});  // Hypotenuse
brd.createElement('line',[p2,p3],{straightFirst:false,straightLast:false,strokeColor:'red'});    // sin
+
brd.create('line',[p2,p3],{straightFirst:false,straightLast:false,strokeColor:'red'});    // sin
brd.createElement('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'});    // cos
+
brd.create('line',[p2,p4],{straightFirst:false,straightLast:false,strokeColor:'red'});    // cos
  
var t = brd.createElement('tangent',[p2],{visible:false});
+
var t = brd.create('tangent',[p2],{visible:false});
var p5 = brd.createElement('point',[brd.intersectionFunc(t,ax,0)],{visible:false,name:'',withLabel:false});
+
var p5 = brd.create('intersection',[t,ax,0],{visible:false,name:'',withLabel:false});
var p6 = brd.createElement('point',[brd.intersectionFunc(t,ay,0)],{visible:false,name:'',withLabel:false});
+
var p6 = brd.create('intersection',[t,ay,0],{visible:false,name:'',withLabel:false});
brd.createElement('line',[p5,p6],{straightFirst:false,straightLast:false});                      // tan + cot
+
brd.create('line',[p5,p6],{straightFirst:false,straightLast:false});                      // tan + cot
brd.createElement('line',[p0,p6],{straightFirst:false,straightLast:false,strokeColor:'green'});  // csc
+
brd.create('line',[p0,p6],{straightFirst:false,straightLast:false,strokeColor:'green'});  // csc
brd.createElement('line',[p0,p5],{straightFirst:false,straightLast:false,strokeColor:'green'});  // sec
+
brd.create('line',[p0,p5],{straightFirst:false,straightLast:false,strokeColor:'green'});  // sec
  
brd.createElement('text',[
+
brd.create('text',[
 
         function(){return (p0.X()+p2.X())*0.5;},
 
         function(){return (p0.X()+p2.X())*0.5;},
 
         function(){return (p0.Y()+p2.Y())*0.5;},
 
         function(){return (p0.Y()+p2.Y())*0.5;},
 
         '1'],{});
 
         '1'],{});
  
brd.createElement('text',[
+
brd.create('text',[
 
         function(){return (p2.X()+p4.X())*0.3;},
 
         function(){return (p2.X()+p4.X())*0.3;},
 
         function(){return (p2.Y()+p4.Y())*0.5;},
 
         function(){return (p2.Y()+p4.Y())*0.5;},
 
         'cos'],{});
 
         'cos'],{});
  
brd.createElement('text',[
+
brd.create('text',[
 
         function(){return (p2.X()+p3.X())*0.5;},
 
         function(){return (p2.X()+p3.X())*0.5;},
 
         function(){return (p2.Y()+p3.Y())*0.5;},
 
         function(){return (p2.Y()+p3.Y())*0.5;},
 
         'sin'],{});
 
         'sin'],{});
  
brd.createElement('text',[
+
brd.create('text',[
 
         function(){return 0.1+(p2.X()+p5.X())*0.5;},
 
         function(){return 0.1+(p2.X()+p5.X())*0.5;},
 
         function(){return 0.1+(p2.Y()+p5.Y())*0.5;},
 
         function(){return 0.1+(p2.Y()+p5.Y())*0.5;},
 
         'tan'],{});
 
         'tan'],{});
  
brd.createElement('text',[
+
brd.create('text',[
 
         function(){return 0.1+(p2.X()+p6.X())*0.5;},
 
         function(){return 0.1+(p2.X()+p6.X())*0.5;},
 
         function(){return 0.1+(p2.Y()+p6.Y())*0.5;},
 
         function(){return 0.1+(p2.Y()+p6.Y())*0.5;},
 
         'cot'],{});
 
         'cot'],{});
  
brd.createElement('text',[
+
brd.create('text',[
 
         function(){return -0.2+(p0.X()+p6.X())*0.5;},
 
         function(){return -0.2+(p0.X()+p6.X())*0.5;},
 
         function(){return (p0.Y()+p6.Y())*0.5;},
 
         function(){return (p0.Y()+p6.Y())*0.5;},
 
         'csc'],{});
 
         'csc'],{});
  
brd.createElement('text',[
+
brd.create('text',[
 
         function(){return (p0.X()+p5.X())*0.5;},
 
         function(){return (p0.X()+p5.X())*0.5;},
 
         function(){return (p0.Y()+p5.Y())*0.5;},
 
         function(){return (p0.Y()+p5.Y())*0.5;},
Line 65: Line 65:
 
</jsxgraph>
 
</jsxgraph>
  
 +
===The JavaScript Code===
 +
<source lang="javascript">
 +
</source>
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Geometry]]
 
[[Category:Geometry]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

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