# Power Series for sine and cosine

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## Power Series for Sine

$\displaystyle{ \sum_{k=0}^n (-1)^k\frac{1}{(2k+1)!}x^{2k+1} }$

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();