Power Series for sine and cosine: Difference between revisions

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Line 2: Line 2:
:<math>\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}</math>
:<math>\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}</math>


<html>
<jsxgraph box="jxgbox1" width="700" height="300">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, boundingbox: [-6, 3, 8, -3]});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jxgbox1" class="jxgbox" style="width:700px; height:300px;"></div>
<script language="JavaScript">
// Board
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
board1.suspendUpdate();
board1.createElement('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
board1.create('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});
var s = board1.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
board1.createElement('functiongraph', [
board1.create('functiongraph', [
function(t) {
function(t) {
var val = 0, i, sv = s.Value()+1;
var val = 0, i, sv = s.Value()+1;
for(i = 0; i < sv; i++) {
for(i = 0; i < sv; i++) {
   val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
   val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / JXG.Math.factorial(2*i+1);
}
}
return val;
return val;
Line 22: Line 17:
-10, 10], {strokeColor: "#bb0000"});
-10, 10], {strokeColor: "#bb0000"});
board1.unsuspendUpdate();
board1.unsuspendUpdate();
/*
</jsxgraph>  
*/
</script>
</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/jsxgraphcore.js"></script>
<div id="jxgbox1" class="jxgbox" style="width:700px; height:600px;"></div>
</source>


<source lang="javascript">
<source lang="javascript">
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, boundingbox: [-6, 3, 8, -3]});
board1.suspendUpdate();
board1.suspendUpdate();
board1.createElement('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
board1.create('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});
var s = board1.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
board1.createElement('functiongraph', [
board1.create('functiongraph', [
   function(t) {
   function(t) {
     var val = 0, i, sv = s.Value()+1;
     var val = 0, i, sv = s.Value()+1;
     for(i = 0; i < sv; i++) {
     for(i = 0; i < sv; i++) {
       val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
       val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / JXG.Math.factorial(2*i+1);
     }
     }
     return val;
     return val;
Line 50: Line 37:


== Power Series for Cosine ==
== Power Series for Cosine ==
<html>
<jsxgraph box="jxgbox2" width="700" height="300">
<div id="jxgbox2" class="jxgbox" style="width:700px; height:300px;"></div>
board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, boundingbox: [-6, 3, 8, -3]});
<script language="JavaScript">
// Board
board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
board2.suspendUpdate();
board2.createElement('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
board2.create('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});
var s2 = board2.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1});
board2.createElement('functiongraph', [
board2.create('functiongraph', [
function(t) {
function(t) {
var val = 0, i, sv = s2.Value()+1;
var val = 0, i, sv = s2.Value()+1;
for(i = 0; i < sv; i++) {
for(i = 0; i < sv; 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) / JXG.Math.factorial(2*i);
}
}
return val;
return val;
Line 68: Line 52:
-10, 10],{strokeColor: "#009900"});
-10, 10],{strokeColor: "#009900"});
board2.unsuspendUpdate();
board2.unsuspendUpdate();
</script>
</jsxgraph>
</html>


<source lang="javascript">
<source lang="javascript">
board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, originX: 300, originY: 150, unitX: 50, unitY: 50});
board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, boundingbox: [-6, 3, 8, -3]});
board2.suspendUpdate();
board2.suspendUpdate();
board2.createElement('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
board2.create('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});
var s2 = board2.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1});
board2.createElement('functiongraph', [
board2.create('functiongraph', [
   function(t) {
   function(t) {
     var val = 0, i, sv = Math.floor(s2.Value())+1;
     var val = 0, i, sv = Math.floor(s2.Value())+1;
     for(i = 0; i < sv; i++) {
     for(i = 0; i < sv; 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) / JXG.Math.factorial(2*i);
     }
     }
     return val;
     return val;

Latest revision as of 15:42, 20 February 2013

Power Series for Sine

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

board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, boundingbox: [-6, 3, 8, -3]});
board1.suspendUpdate();
board1.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
var s = board1.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
board1.create('functiongraph', [
  function(t) {
    var val = 0, i, sv = s.Value()+1;
    for(i = 0; i < sv; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / JXG.Math.factorial(2*i+1);
    }
    return val;
  }, -10, 10], {strokeColor: "#bb0000"});
board1.unsuspendUpdate();


Power Series for Cosine

board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, boundingbox: [-6, 3, 8, -3]});
board2.suspendUpdate();
board2.create('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
var s2 = board2.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1});
board2.create('functiongraph', [
  function(t) {
    var val = 0, i, sv = Math.floor(s2.Value())+1;
    for(i = 0; i < sv; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / JXG.Math.factorial(2*i);
    }
    return val;
  }, -10, 10],{strokeColor: "#009900"});						
board2.unsuspendUpdate();

References

Retrieved from "http://jsxgraph.org/wiki/index.php?title=Power_Series_for_sine_and_cosine&oldid=6002"