El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\operatorname{atan}{\left(\sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{\sqrt{2}} \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - 2 \operatorname{atan}{\left(\sqrt{2} + \sqrt{3} \right)}$$
$$x_{2} = - 2 \operatorname{atan}{\left(- \sqrt{3} + \sqrt{2} \right)}$$
Solución numérica$$x_{1} = 72.8721107412356$$
$$x_{2} = 0.615479708670387$$
$$x_{3} = -55.9331880559459$$
$$x_{4} = -21.3756688664582$$
$$x_{5} = -18.2340762128684$$
$$x_{6} = -52.7915954023561$$
$$x_{7} = -43.3668174415867$$
$$x_{8} = 60.3057401268765$$
$$x_{9} = 79.1552960484152$$
$$x_{10} = 54.0225548196969$$
$$x_{11} = 6.89866501584997$$
$$x_{12} = -46.5084100951765$$
$$x_{13} = -33.9420394808173$$
$$x_{14} = -93.6322998990234$$
$$x_{15} = 41.4561842053377$$
$$x_{16} = 16.3234429766194$$
$$x_{17} = -77.9243366310744$$
$$x_{18} = 19.4650356302091$$
$$x_{19} = -40.2252247879969$$
$$x_{20} = 44.5977768589275$$
$$x_{21} = -15.0924835592786$$
$$x_{22} = -65.3579660167153$$
$$x_{23} = 57.1641474732867$$
$$x_{24} = 47.7393695125173$$
$$x_{25} = -81.0659292846642$$
$$x_{26} = 69.7305180876458$$
$$x_{27} = -99.915485206203$$
$$x_{28} = 22.6066282837989$$
$$x_{29} = -90.4907072454336$$
$$x_{30} = 91.7216666627744$$
$$x_{31} = 28.8898135909785$$
$$x_{32} = -87.3491145918438$$
$$x_{33} = -71.6411513238949$$
$$x_{34} = 66.5889254340561$$
$$x_{35} = 88.5800740091846$$
$$x_{36} = -37.0836321344071$$
$$x_{37} = 25.7482209373887$$
$$x_{38} = -2506.37545785598$$
$$x_{39} = 38.3145915517479$$
$$x_{40} = 13.1818503230296$$
$$x_{41} = 82.296888702005$$
$$x_{42} = -59.0747807095357$$
$$x_{43} = 98.004851969954$$
$$x_{44} = -5.6677055985092$$
$$x_{45} = -11.9508909056888$$
$$x_{46} = -30.8004468272275$$
$$x_{47} = 63.4473327804663$$
$$x_{48} = -24.517261520048$$
$$x_{49} = 10.0402576694398$$
$$x_{50} = -2.52611294491941$$
$$x_{51} = -49.6500027487663$$
$$x_{52} = 85.4384813555948$$
$$x_{53} = 32.0314062445683$$
$$x_{54} = -8.80929825209899$$
$$x_{55} = 101.146444623544$$
$$x_{56} = -62.2163733631255$$
$$x_{57} = 76.0137033948254$$
$$x_{58} = -68.4995586703051$$
$$x_{59} = 35.1729988981581$$
$$x_{60} = -74.7827439774847$$
$$x_{61} = 50.8809621661071$$
$$x_{62} = 94.8632593163642$$
$$x_{63} = -84.207521938254$$
$$x_{64} = -96.7738925526132$$
$$x_{65} = 3.75707236226018$$
$$x_{66} = -27.6588541736378$$