JSXGraph Wiki - User contributions [en]

Power Series for sine and cosine

2008-09-17T15:24:55Z

84.147.114.36:

== Power Series for Sine ==
<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>
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
// Axes and Properties
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();
/*
*/
</script>
</html>

<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>

== Power Series for Cosine ==
<html>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
// Axes and Properties
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();
</script>
</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]]

Power Series for sine and cosine

2008-09-17T15:24:10Z

84.147.114.36:

== Power Series for Sine ==
<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>
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
// Axes and Properties
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();
/*
*/
</script>
</html>
== Source code of this example ==
<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>

== Power Series for Cosine ==
<html>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
// Axes and Properties
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();
</script>
</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]]

Power Series for sine and cosine

2008-09-17T15:22:17Z

84.147.114.36:

== Power Series for Sine ==
<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>
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
// Axes and Properties
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();
/*
*/
</script>
</html>
=== test ===
<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>

== Power Series for Cosine ==
<html>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
// Axes and Properties
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();
</script>
</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]]

Power Series for sine and cosine

2008-09-17T15:21:17Z

84.147.114.36:

== Power Series for Sine ==
<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>
<div id="jxgbox1" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
// Axes and Properties
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();
/*
*/
</script>
<br clear=all>
</html>

<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>

== Power Series for Cosine ==
<html>
<div id="jxgbox2" class="jxgbox" style="width:600px; height:300px;"></div>
<script language="JavaScript">
// Board
board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
// Axes and Properties
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();
</script>
</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]]