Rolling circle on cosine

The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('jxgbox',{boundingbox:[-1,5,20,-1], keepaspectratio:true});
brd.suspendUpdate();

// Line
var line = brd.create('curve', [function(t) { return t;}, function(t){ return 0.5*Math.cos(t);}], 
{strokeWidth:6, strokeColor:'green'});

// Circle
var P = brd.create('point',[0,0.5],{name:'P', trace:false});
var C = brd.create('point',[0,1],{name:'C'});
var circle = brd.create('curve',[
                    function(t){var d = P.Dist(C),
                                    beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
                                t += beta;
                                return C.X()+d*Math.cos(t);
                    },
                    function(t){var d = P.Dist(C), 
                                    beta = JXG.Math.Geometry.rad([C.X()+1,C.Y()],C,P);
                                t += beta;
                                return C.Y()+d*Math.sin(t);
                    },
                    0,2*Math.PI],
                    {strokeWidth:6, strokeColor:'green'});

// Point on circle
var B = brd.create('glider',[0,1.5,circle],{name:'B', color:'blue',trace:true});
brd.create('segment',[C,B],{color:'black'}); 
brd.unsuspendUpdate();
var rol = brd.createRoulette(line, circle, 0, Math.PI/18, 1, 150, [C,P,B]);