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

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Line 1: Line 1:
 
== 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" />
Line 33: Line 52:
 
</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>
Line 80: Line 98:
 
</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 16:27, 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();