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

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(New page: <html> <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/pro...)
 
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<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/prototype.js"></script>
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
+
<script language="JavaScript">
<script language="JavaScript">
+
// Board
// Board
+
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 30, unitY: 30});
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 30, unitY: 30});
+
board1.suspendUpdate();
board1.suspendUpdate();
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// Axes and Properties
// Axes and Properties
+
board1.createElement('axis', [[1,0], [0,0]], {});
board1.createElement('axis', [[1,0], [0,0]], {});
+
board1.createElement('axis', [[0,1], [0,0]], {});
board1.createElement('axis', [[0,1], [0,0]], {});
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board1.snapToGrid = true;
board1.snapToGrid = true;
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//
//
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board1.createElement('curve', [function(t){ return t; }, function(t){ return Math.sin(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
board1.createElement('curve', [function(t){ return t; }, function(t){ return Math.sin(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
+
//
//
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var s = board1.createElement('slider', [2,-4,5,0,10,0], {name:'S'});
var s = board1.createElement('slider', [2,-4,5,0,10,0], {name:'S'});
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//
//
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board1.createElement('curve', [
board1.createElement('curve', [
+
function(t){ return t; },  
function(t){ return t; },  
+
function(t) {
function(t) {
+
var val = 0;
var val = 0;
+
for(var i = 0; i < Math.floor(s.X()) + 1; i++) {
for(var i = 0; i < Math.floor(s.X()) + 1; i++) {
+
var f = 1;
var f = 1;
+
var n = 1;
var n = 1;
+
while (n <= 2 * i + 1) { f = f * n++; }
while (n <= 2 * i + 1) { f = f * n++; }
+
  val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / f;
    val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / f;
+
}
}
+
return val;
return val;
+
},
},
+
"t", -10, 10], {strokeColor: "#bb0000"});
"t", -10, 10], {strokeColor: "#bb0000"});
+
board1.unsuspendUpdate();
board1.unsuspendUpdate();
+
/*
/*
+
*/
*/
+
</script>  
</script>  
+
<h2>Power Series for Cosine</h2>
<h2>Power Series for Cosine</h2>
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<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
+
<script language="JavaScript">
<script language="JavaScript">
+
// Board
// Board
+
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 30, unitY: 30});
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 30, unitY: 30});
+
board2.suspendUpdate();
board2.suspendUpdate();
+
// Axes and Properties
// Axes and Properties
+
board2.createElement('axis', [[1,0], [0,0]], {});
board2.createElement('axis', [[1,0], [0,0]], {});
+
board2.createElement('axis', [[0,1], [0,0]], {});
board2.createElement('axis', [[0,1], [0,0]], {});
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board2.snapToGrid = true;
board2.snapToGrid = true;
+
//
//
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board2.createElement('curve', [function(t){ return t; }, function(t){ return Math.cos(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
board2.createElement('curve', [function(t){ return t; }, function(t){ return Math.cos(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
+
//
//
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var s2 = board2.createElement('slider', [2,-4,5,0,10,0], {name:'T'});
var s2 = board2.createElement('slider', [2,-4,5,0,10,0], {name:'T'});
+
//
//
+
board2.createElement('curve', [
board2.createElement('curve', [
+
function(t){ return t; },  
function(t){ return t; },  
+
function(t) {
function(t) {
+
var val = 0;
var val = 0;
+
for(var i = 0; i < Math.floor(s2.X()) + 1; i++) {
for(var i = 0; i < Math.floor(s2.X()) + 1; i++) {
+
var f = 1;
var f = 1;
+
var n = 1;
var n = 1;
+
while (n <= 2 * i) { f = f * n++; }
while (n <= 2 * i) { f = f * n++; }
+
  val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / f;
    val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / f;
+
}
}
+
return val;
return val;
+
},
},
+
"t", -10, 10],{strokeColor: "#009900"});
"t", -10, 10],{strokeColor: "#009900"});
+
board2.unsuspendUpdate();
board2.unsuspendUpdate();
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</script>
</script>
 

Revision as of 12:10, 17 September 2008

<html> <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> <script language="JavaScript"> // Board board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 30, unitY: 30}); board1.suspendUpdate(); // Axes and Properties board1.createElement('axis', [[1,0], [0,0]], {}); board1.createElement('axis', [[0,1], [0,0]], {}); board1.snapToGrid = true; // board1.createElement('curve', [function(t){ return t; }, function(t){ return Math.sin(t); }, "t", -10, 10],{strokeColor: "#cccccc"}); // var s = board1.createElement('slider', [2,-4,5,0,10,0], {name:'S'}); // board1.createElement('curve', [ function(t){ return t; }, function(t) { var val = 0; for(var i = 0; i < Math.floor(s.X()) + 1; i++) { var f = 1; var n = 1; while (n <= 2 * i + 1) { f = f * n++; }

  			val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / f;

} return val; }, "t", -10, 10], {strokeColor: "#bb0000"}); board1.unsuspendUpdate(); /*

  • /

</script>

Power Series for Cosine

<script language="JavaScript"> // Board board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 30, unitY: 30}); board2.suspendUpdate(); // Axes and Properties board2.createElement('axis', [[1,0], [0,0]], {}); board2.createElement('axis', [[0,1], [0,0]], {}); board2.snapToGrid = true; // board2.createElement('curve', [function(t){ return t; }, function(t){ return Math.cos(t); }, "t", -10, 10],{strokeColor: "#cccccc"}); // var s2 = board2.createElement('slider', [2,-4,5,0,10,0], {name:'T'}); // board2.createElement('curve', [ function(t){ return t; }, function(t) { var val = 0; for(var i = 0; i < Math.floor(s2.X()) + 1; i++) { var f = 1; var n = 1; while (n <= 2 * i) { f = f * n++; }

  			val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / f;

} return val; }, "t", -10, 10],{strokeColor: "#009900"}); board2.unsuspendUpdate(); </script>