Power Series for sine and cosine

Power Series for Sine

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<div id="jxgbox1" class="jxgbox" style="width:600px; height:600px;"></div>

board1 = JXG.JSXGraph.initBoard('jxgbox1', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board1.suspendUpdate();
board1.createElement('axis', [[0,0], [1,0]], {});
board1.createElement('axis', [[0,0], [0,1]], {});
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],[5.75,-2.5],[0,0,10]], {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();

Power Series for Cosine

board2 = JXG.JSXGraph.initBoard('jxgbox2', {originX: 300, originY: 150, unitX: 50, unitY: 50});
board2.suspendUpdate();
board2.createElement('axis', [[0,0], [1,0]], {});
board2.createElement('axis', [[0,0], [0,1]], {});
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],[5.75,-2.5],[0,0,10]], {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();

References

• http://en.wikipedia.org/wiki/Trigonometric_functions