Difference between revisions of "Power Series for sine and cosine"

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== Power Series for Sine ==
 
== Power Series for Sine ==
<source lang="html4strict">
+
:<math>\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}</math>
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
<div id="jxgbox1" class="jxgbox" style="width:700px; height:600px;"></div>
 
</source>
 
 
 
<source lang="javascript">
 
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
 
board1.suspendUpdate();
 
board1.createElement('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
 
var s = board1.createElement('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
 
board1.createElement('functiongraph', [
 
  function(t) {
 
    var val = 0;
 
    for(var i = 0; i < s.Value()+1; i++) {
 
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
 
    }
 
    return val;
 
  }, -10, 10], {strokeColor: "#bb0000"});
 
board1.unsuspendUpdate();
 
</source>
 
  
 
<html>
 
<html>
Line 48: Line 27:
 
</script>  
 
</script>  
 
</html>
 
</html>
 +
<source lang="html4strict">
 +
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 +
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 +
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 +
<div id="jxgbox1" class="jxgbox" style="width:700px; height:600px;"></div>
 +
</source>
  
== Power Series for Cosine ==
 
 
<source lang="javascript">
 
<source lang="javascript">
board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
+
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
+
board1.suspendUpdate();
board2.createElement('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
+
board1.createElement('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
var s2 = board2.createElement('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1});
+
var s = board1.createElement('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
board2.createElement('functiongraph', [
+
board1.createElement('functiongraph', [
 
   function(t) {
 
   function(t) {
 
     var val = 0;
 
     var val = 0;
     for(var i = 0; i < Math.floor(s2.Value()) + 1; i++) {
+
     for(var i = 0; i < s.Value()+1; i++) {
       val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / board2.factorial(2*i);
+
       val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
 
     }
 
     }
 
     return val;
 
     return val;
   }, -10, 10],{strokeColor: "#009900"});
+
   }, -10, 10], {strokeColor: "#bb0000"});
board2.unsuspendUpdate();
+
board1.unsuspendUpdate();
 
</source>
 
</source>
 +
 +
 +
== Power Series for Cosine ==
 
<html>
 
<html>
 
<div id="jxgbox2" class="jxgbox" style="width:700px; height:300px;"></div>
 
<div id="jxgbox2" class="jxgbox" style="width:700px; height:300px;"></div>
Line 85: Line 72:
 
</script>
 
</script>
 
</html>
 
</html>
 +
 +
<source lang="javascript">
 +
board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
 +
board2.suspendUpdate();
 +
board2.createElement('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
 +
var s2 = board2.createElement('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1});
 +
board2.createElement('functiongraph', [
 +
  function(t) {
 +
    var val = 0;
 +
    for(var i = 0; i < Math.floor(s2.Value()) + 1; i++) {
 +
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / board2.factorial(2*i);
 +
    }
 +
    return val;
 +
  }, -10, 10],{strokeColor: "#009900"});
 +
board2.unsuspendUpdate();
 +
</source>
  
 
=== References ===
 
=== References ===

Revision as of 14:45, 9 July 2009

Power Series for Sine

[math]\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}[/math]

<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jxgbox1" class="jxgbox" style="width:700px; height:600px;"></div>
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
board1.createElement('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
var s = board1.createElement('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
board1.createElement('functiongraph', [
  function(t) {
    var val = 0;
    for(var i = 0; i < s.Value()+1; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
    }
    return val;
  }, -10, 10], {strokeColor: "#bb0000"});
board1.unsuspendUpdate();


Power Series for Cosine

board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
board2.createElement('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
var s2 = board2.createElement('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1});
board2.createElement('functiongraph', [
  function(t) {
    var val = 0;
    for(var i = 0; i < Math.floor(s2.Value()) + 1; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / board2.factorial(2*i);
    }
    return val;
  }, -10, 10],{strokeColor: "#009900"});						
board2.unsuspendUpdate();

References