El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$- \frac{\sqrt{2}}{2} \cot{\left(x \right)} + \frac{\sqrt{2}}{2} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{\pi}{4}$$
Solución numérica$$x_{1} = -99.7455667514759$$
$$x_{2} = 73.0420291959627$$
$$x_{3} = -96.6039740978861$$
$$x_{4} = -8.63937979737193$$
$$x_{5} = -24.3473430653209$$
$$x_{6} = -71.4712328691678$$
$$x_{7} = 76.1836218495525$$
$$x_{8} = -30.6305283725005$$
$$x_{9} = -5.49778714378214$$
$$x_{10} = 3.92699081698724$$
$$x_{11} = -62.0464549083984$$
$$x_{12} = -33.7721210260903$$
$$x_{13} = -36.9137136796801$$
$$x_{14} = -87.1791961371168$$
$$x_{15} = 95.0331777710912$$
$$x_{16} = -40.0553063332699$$
$$x_{17} = -58.9048622548086$$
$$x_{18} = 38.484510006475$$
$$x_{19} = -84.037603483527$$
$$x_{20} = 66.7588438887831$$
$$x_{21} = -43.1968989868597$$
$$x_{22} = 51.0508806208341$$
$$x_{23} = 0.785398163397448$$
$$x_{24} = 69.9004365423729$$
$$x_{25} = -27.4889357189107$$
$$x_{26} = 85.6083998103219$$
$$x_{27} = 54.1924732744239$$
$$x_{28} = 13.3517687777566$$
$$x_{29} = 88.7499924639117$$
$$x_{30} = 98.174770424681$$
$$x_{31} = -21.2057504117311$$
$$x_{32} = -68.329640215578$$
$$x_{33} = 10.2101761241668$$
$$x_{34} = -11.7809724509617$$
$$x_{35} = 19.6349540849362$$
$$x_{36} = 41.6261026600648$$
$$x_{37} = -55.7632696012188$$
$$x_{38} = 35.3429173528852$$
$$x_{39} = 82.4668071567321$$
$$x_{40} = -93.4623814442964$$
$$x_{41} = -90.3207887907066$$
$$x_{42} = 44.7676953136546$$
$$x_{43} = -49.4800842940392$$
$$x_{44} = -74.6128255227576$$
$$x_{45} = 32.2013246992954$$
$$x_{46} = -2.35619449019234$$
$$x_{47} = -65.1880475619882$$
$$x_{48} = 57.3340659280137$$
$$x_{49} = 22.776546738526$$
$$x_{50} = 79.3252145031423$$
$$x_{51} = 63.6172512351933$$
$$x_{52} = -46.3384916404494$$
$$x_{53} = 29.0597320457056$$
$$x_{54} = 25.9181393921158$$
$$x_{55} = -52.621676947629$$
$$x_{56} = -14.9225651045515$$
$$x_{57} = 47.9092879672443$$
$$x_{58} = 60.4756585816035$$
$$x_{59} = 16.4933614313464$$
$$x_{60} = -77.7544181763474$$
$$x_{61} = 91.8915851175014$$
$$x_{62} = -80.8960108299372$$
$$x_{63} = 7.06858347057703$$
$$x_{64} = -18.0641577581413$$