Difference between revisions of "Power Series for sine and cosine"
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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 box="jxgbox1" width="700" height="300"> | |
| − | + | board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, boundingbox: [-6, 3, 8, -3]}); | |
| − | + | board1.suspendUpdate(); | |
| − | </ | + | board1.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"}); |
| + | var s = board1.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1}); | ||
| + | board1.create('functiongraph', [ | ||
| + | function(t) { | ||
| + | var val = 0, i, sv = s.Value()+1; | ||
| + | for(i = 0; i < sv; i++) { | ||
| + | val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / JXG.Math.factorial(2*i+1); | ||
| + | } | ||
| + | return val; | ||
| + | }, | ||
| + | -10, 10], {strokeColor: "#bb0000"}); | ||
| + | board1.unsuspendUpdate(); | ||
| + | </jsxgraph> | ||
<source lang="javascript"> | <source lang="javascript"> | ||
| − | board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, | + | board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, boundingbox: [-6, 3, 8, -3]}); |
board1.suspendUpdate(); | board1.suspendUpdate(); | ||
| − | board1. | + | board1.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"}); |
| − | var s = board1. | + | var s = board1.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1}); |
| − | board1. | + | board1.create('functiongraph', [ |
function(t) { | function(t) { | ||
| − | var val = 0; | + | var val = 0, i, sv = s.Value()+1; |
| − | for( | + | for(i = 0; i < sv; i++) { |
| − | val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / | + | val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / JXG.Math.factorial(2*i+1); |
} | } | ||
return val; | return val; | ||
| Line 23: | Line 35: | ||
</source> | </source> | ||
| − | + | ||
| − | + | == Power Series for Cosine == | |
| − | + | <jsxgraph box="jxgbox2" width="700" height="300"> | |
| − | < | + | board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, boundingbox: [-6, 3, 8, -3]}); |
| − | + | board2.suspendUpdate(); | |
| − | + | board2.create('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"}); | |
| − | + | var s2 = board2.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1}); | |
| − | + | board2.create('functiongraph', [ | |
| − | |||
| − | |||
| − | var | ||
| − | |||
function(t) { | function(t) { | ||
| − | var val = 0; | + | var val = 0, i, sv = s2.Value()+1; |
| − | for( | + | for(i = 0; i < sv; i++) { |
| − | val = val + Math.pow(-1, i) * Math.pow(t, 2 * i | + | val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / JXG.Math.factorial(2*i); |
} | } | ||
return val; | return val; | ||
}, | }, | ||
| − | -10, 10], {strokeColor: "# | + | -10, 10],{strokeColor: "#009900"}); |
| − | + | board2.unsuspendUpdate(); | |
| − | + | </jsxgraph> | |
| − | |||
| − | |||
| − | </ | ||
| − | |||
<source lang="javascript"> | <source lang="javascript"> | ||
| − | board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, | + | board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, boundingbox: [-6, 3, 8, -3]}); |
board2.suspendUpdate(); | board2.suspendUpdate(); | ||
| − | board2. | + | board2.create('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"}); |
| − | var s2 = board2. | + | var s2 = board2.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1}); |
| − | board2. | + | board2.create('functiongraph', [ |
function(t) { | function(t) { | ||
| − | var val = 0 | + | var val = 0, i, sv = Math.floor(s2.Value())+1; |
| − | + | for(i = 0; i < sv; i++) { | |
| − | val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / | + | val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / JXG.Math.factorial(2*i); |
} | } | ||
return val; | return val; | ||
| Line 65: | Line 69: | ||
board2.unsuspendUpdate(); | board2.unsuspendUpdate(); | ||
</source> | </source> | ||
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=== References === | === References === | ||
Latest revision as of 17:42, 20 February 2013
Power Series for Sine
- [math]\sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1}[/math]
board1 = JXG.JSXGraph.initBoard('jxgbox1', {axis:true, boundingbox: [-6, 3, 8, -3]});
board1.suspendUpdate();
board1.create('functiongraph', [function(t){ return Math.sin(t); },-10, 10],{strokeColor: "#cccccc"});
var s = board1.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'S',snapWidth:1});
board1.create('functiongraph', [
function(t) {
var val = 0, i, sv = s.Value()+1;
for(i = 0; i < sv; i++) {
val = val + Math.pow(-1, i) * Math.pow(t, 2 * i + 1) / JXG.Math.factorial(2*i+1);
}
return val;
}, -10, 10], {strokeColor: "#bb0000"});
board1.unsuspendUpdate();
Power Series for Cosine
board2 = JXG.JSXGraph.initBoard('jxgbox2', {axis:true, boundingbox: [-6, 3, 8, -3]});
board2.suspendUpdate();
board2.create('functiongraph', [function(t){ return Math.cos(t); }, -10, 10],{strokeColor: "#cccccc"});
var s2 = board2.create('slider', [[0.75,-1.5],[5.75,-1.5],[0,0,10]], {name:'T',snapWidth:1});
board2.create('functiongraph', [
function(t) {
var val = 0, i, sv = Math.floor(s2.Value())+1;
for(i = 0; i < sv; i++) {
val = val + Math.pow(-1, i) * Math.pow(t, 2 * i) / JXG.Math.factorial(2*i);
}
return val;
}, -10, 10],{strokeColor: "#009900"});
board2.unsuspendUpdate();
