Power Series for sine and cosine: Difference between revisions

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== Power Series for Sine ==
== Power Series for Sine ==
<source lang="javascript">
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
board1.createElement('axis', [[1,0], [0,0]], {});
board1.createElement('axis', [[0,1], [0,0]], {});
board1.createElement('curve', [function(t){ return t; }, function(t){ return Math.sin(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
var s = board1.createElement('slider', [0.75,-2.5,5,0,10,0], {name:'S'});
board1.createElement('curve', [
  't',
  function(t) {
    var val = 0;
    for(var i = 0; i < Math.floor(s.X()) + 1; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
    }
    return val;
  }, "t", -10, 10], {strokeColor: "#bb0000", curveType:'plot'});
board1.unsuspendUpdate();
</source>
<html>
<html>
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
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</html>
</html>


== Power Series for Cosine ==
<source lang="javascript">
<source lang="javascript">
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
board2.suspendUpdate();
board1.createElement('axis', [[1,0], [0,0]], {});
board2.createElement('axis', [[1,0], [0,0]], {});
board1.createElement('axis', [[0,1], [0,0]], {});
board2.createElement('axis', [[0,1], [0,0]], {});
board1.createElement('curve', [function(t){ return t; }, function(t){ return Math.sin(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
board2.createElement('curve', [function(t){ return t; }, function(t){ return Math.cos(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
var s = board1.createElement('slider', [0.75,-2.5,5,0,10,0], {name:'S'});
var s2 = board2.createElement('slider', [0.75,-2.5,5,0,10,0], {name:'T'});
board1.createElement('curve', [
board2.createElement('curve', [
   't',  
   '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(s2.X()) + 1; 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) / board2.factorial(2*i);
     }
     }
     return val;
     return val;
   }, "t", -10, 10], {strokeColor: "#bb0000", curveType:'plot'});
   }, "t", -10, 10],{strokeColor: "#009900", curveType:'plot'});
board1.unsuspendUpdate();
board2.unsuspendUpdate();
</source>
</source>
== Power Series for Cosine ==
<html>
<html>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
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</script>
</script>
</html>
</html>
<source lang="javascript">
 
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
board2.createElement('axis', [[1,0], [0,0]], {});
board2.createElement('axis', [[0,1], [0,0]], {});
board2.createElement('curve', [function(t){ return t; }, function(t){ return Math.cos(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
var s2 = board2.createElement('slider', [0.75,-2.5,5,0,10,0], {name:'T'});
board2.createElement('curve', [
  't',
  function(t) {
    var val = 0;
    for(var i = 0; i < Math.floor(s2.X()) + 1; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / board2.factorial(2*i);
    }
    return val;
  }, "t", -10, 10],{strokeColor: "#009900", curveType:'plot'});
board2.unsuspendUpdate();
</source>


[[Category:Examples]]
[[Category:Examples]]

Revision as of 15:27, 17 September 2008

Power Series for Sine

board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
board1.createElement('axis', [[1,0], [0,0]], {});
board1.createElement('axis', [[0,1], [0,0]], {});
board1.createElement('curve', [function(t){ return t; }, function(t){ return Math.sin(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
var s = board1.createElement('slider', [0.75,-2.5,5,0,10,0], {name:'S'});
board1.createElement('curve', [
  't', 
  function(t) {
    var val = 0;
    for(var i = 0; i < Math.floor(s.X()) + 1; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / board1.factorial(2*i+1);
    }
    return val;
  }, "t", -10, 10], {strokeColor: "#bb0000", curveType:'plot'});
board1.unsuspendUpdate();

Power Series for Cosine

board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
board2.createElement('axis', [[1,0], [0,0]], {});
board2.createElement('axis', [[0,1], [0,0]], {});
board2.createElement('curve', [function(t){ return t; }, function(t){ return Math.cos(t); }, "t", -10, 10],{strokeColor: "#cccccc"});
var s2 = board2.createElement('slider', [0.75,-2.5,5,0,10,0], {name:'T'});
board2.createElement('curve', [
  't', 
  function(t) {
    var val = 0;
    for(var i = 0; i < Math.floor(s2.X()) + 1; i++) {
      val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / board2.factorial(2*i);
    }
    return val;
  }, "t", -10, 10],{strokeColor: "#009900", curveType:'plot'});						
board2.unsuspendUpdate();