Difference between revisions of "Power Series for sine"

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== Power Series for Sine ==
 
== Power Series for Sine ==
:<math>\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}</math>
+
<jsxgraph with="700" height="400">
 +
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,8,-3]});
 +
var axx = brd.create('axis',[[0,0],[1,0]]);
 +
var axy = brd.create('axis',[[0,0],[0,1]]);
  
<jsxgraph with="700" height="400">
+
brd.suspendUpdate();
 +
brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
 +
var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,1,10]], {name:'S',snapWidth:1});
 +
var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});
 +
brd.create('functiongraph', [
 +
function(t) {
 +
var val = 0, i, sv = s.Value()+1, a;
 +
for(i = 0; i < sv; i++) {
 +
                  if (i%4==0) {
 +
                    a = Math.sin(x0.X());
 +
                  } else if (i%4==1) {
 +
                    a = Math.cos(x0.X());
 +
                  } else if (i%4==2) {
 +
                    a = -Math.sin(x0.X());
 +
                  } else if (i%4==3) {
 +
                    a = -Math.cos(x0.X());
 +
                  }
 +
            val = val + a*Math.pow(t-x0.X(), i) / JXG.Math.factorial(i);
 +
}
 +
return val;
 +
},
 +
-10, 10], {strokeColor: "#bb0000"});
 +
brd.unsuspendUpdate();
 +
</jsxgraph>
 +
 
 +
===The underlying JavaScript code===
 +
<source lang="javascript">
 
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,8,-3]});
 
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,8,-3]});
 
var axx = brd.create('axis',[[0,0],[1,0]]);
 
var axx = brd.create('axis',[[0,0],[1,0]]);
Line 11: Line 40:
 
var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
 
var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
 
var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});
 
var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});
/*
 
 
brd.create('functiongraph', [
 
brd.create('functiongraph', [
 
function(t) {
 
function(t) {
var val = 0, i, sv = s.Value()+1;
+
var val = 0, i, sv = s.Value()+1, a;
 
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);
+
                  if (i%4==0) {
 +
                    a = Math.sin(x0.X());
 +
                  } else if (i%4==1) {
 +
                    a = Math.cos(x0.X());
 +
                  } else if (i%4==2) {
 +
                    a = -Math.sin(x0.X());
 +
                  } else if (i%4==3) {
 +
                    a = -Math.cos(x0.X());
 +
                  }
 +
            val = val + a*Math.pow(t-x0.X(), i) / JXG.Math.factorial(i);
 
}
 
}
 
return val;
 
return val;
 
},
 
},
 
-10, 10], {strokeColor: "#bb0000"});
 
-10, 10], {strokeColor: "#bb0000"});
*/
 
 
brd.unsuspendUpdate();
 
brd.unsuspendUpdate();
 +
</source>
  
</jsxgraph>
+
[[Category:Calculus]]
 +
[[Category:Examples]]

Latest revision as of 17:41, 20 February 2013

Power Series for Sine

The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-7,3,8,-3]});
var axx = brd.create('axis',[[0,0],[1,0]]);
var axy = brd.create('axis',[[0,0],[0,1]]);

brd.suspendUpdate();
brd.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
var s = brd.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
var x0 = brd.create('glider', [0,0,axx], {name:'x_0'});
brd.create('functiongraph', [
	function(t) {
		var val = 0, i, sv = s.Value()+1, a;
		for(i = 0; i < sv; i++) {
                  if (i%4==0) {
                     a = Math.sin(x0.X());
                  } else if (i%4==1) {
                     a = Math.cos(x0.X());
                  } else if (i%4==2) {
                     a = -Math.sin(x0.X());
                  } else if (i%4==3) {
                     a = -Math.cos(x0.X());
                  }
   	          val = val + a*Math.pow(t-x0.X(), i) / JXG.Math.factorial(i);
		}
		return val;
	},
-10, 10], {strokeColor: "#bb0000"});
brd.unsuspendUpdate();