{"version":9,"randomSeed":"5c8b6c1a4eb604530047993dd0edd0c2","graph":{"viewport":{"xmin":-0.5877951313453506,"ymin":-0.5517501194583687,"xmax":11.72618605944646,"ymax":7.9808979575268815}},"expressions":{"list":[{"type":"text","id":"9","text":"the inverse of f(x) approximates iterated sine"},{"type":"text","id":"11","text":"e.g. f(sin(sin(sin(1)))) should = 3"},{"type":"text","id":"18","text":"and no, i didn't find this function myself (thanks, W|A)"},{"type":"expression","id":"6","color":"#000000","latex":"f\\left(x\\right)=-\\int_{1}^{x}\\frac{1}{p-\\sin p}dp","hidden":true},{"type":"expression","id":"15","color":"#c74440","latex":"f\\left(0.23391394784444508\\right)-50"},{"type":"text","id":"13","text":"compute the actual iterated-sine, starting at 1, iterated x1 times, (isin(1, x1)) and save to y1 the difference between x1 and f(isin(1, x1))"},{"id":"4","type":"table","columns":[{"values":["1","2","3","4","5","6","7","8","9","10","15","20","25","30","35","40","45","50","60","70","80","90","100","125","150","175","200"],"hidden":true,"id":"2","color":"#2d70b3","latex":"x_{1}"},{"values":["0.2898","0.4859","0.6365","0.7594","0.8635","0.954","1.0341","1.1061","1.1714","1.2313","1.4728","1.6537","1.7985","1.9195","2.0233","2.1143","2.1954","2.2684","","","","","","","","",""],"id":"3","color":"#388c46","latex":"y_{1}"},{"values":["","","","","","","","","","","","","","","","","","","","","","","","","","",""],"id":"19","color":"#6042a6","latex":"e_{{1}}"}]},{"type":"expression","id":"16","color":"#2d70b3","latex":"y_{1}\\sim a\\ln\\left(bx_{1}+c\\right)","residualVariable":"e_{1}","regressionParameters":{"a":0.7126036116121903,"b":0.4588645689462154,"c":1.0539120630209333}}]}}