Power Series for sine: Difference between revisions

Revision as of 10:37, 28 May 2010

[math]\displaystyle{ \sum_{k=0}^n a_k(x-x_0)^{k} }[/math]

@@ Line 1: / Line 1: @@
 == Power Series for Sine ==
-:<math>\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}</math>
+:<math>\sum_{k=0}^n a_k(x-x_0)^{k}</math>
 <jsxgraph with="700" height="400">
@@ Line 11: / Line 11: @@
 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;
+		var val = 0, i, sv = s.Value()+1, a;
 		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) / brd.factorial(i);
 		}
 		return val;
 	},
 -10, 10], {strokeColor: "#bb0000"});
-*/
 brd.unsuspendUpdate();
 </jsxgraph>