El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(5 \sin{\left(x \right)} - 3 \cos^{2}{\left(x \right)}\right) + \frac{1}{3} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 2 \operatorname{atan}{\left(\frac{15}{16} + \frac{3 \sqrt{57}}{16} + \frac{\sqrt{2} \sqrt{241 + 45 \sqrt{57}}}{16} \right)}$$
$$x_{2} = 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{241 + 45 \sqrt{57}}}{16} + \frac{15}{16} + \frac{3 \sqrt{57}}{16} \right)}$$
Solución numérica$$x_{1} = -68.6761069773767$$
$$x_{2} = 2.70266125199109$$
$$x_{3} = -37.2601804414788$$
$$x_{4} = 69.5539697805741$$
$$x_{5} = -53.8460065126252$$
$$x_{6} = -49.826551055838$$
$$x_{7} = -56.1097363630176$$
$$x_{8} = 34.118587787889$$
$$x_{9} = 59.2513290166074$$
$$x_{10} = -60.1291918198048$$
$$x_{11} = -78.9787477413435$$
$$x_{12} = -22.4300799767273$$
$$x_{13} = -24.6938098271196$$
$$x_{14} = 907.481345485852$$
$$x_{15} = 44.4212285518558$$
$$x_{16} = 63.2707844733946$$
$$x_{17} = -41.279635898266$$
$$x_{18} = 65.534514323787$$
$$x_{19} = -72.6955624341639$$
$$x_{20} = -173.226527349037$$
$$x_{21} = 25.571672630317$$
$$x_{22} = 31.8548579374966$$
$$x_{23} = 0.438931401598704$$
$$x_{24} = 96.9504408596849$$
$$x_{25} = -6999.02950079646$$
$$x_{26} = 84.3840702453257$$
$$x_{27} = -74.9592922845563$$
$$x_{28} = 56.987599166215$$
$$x_{29} = -16.1468946695477$$
$$x_{30} = 140.932738009942$$
$$x_{31} = -34.9964505910864$$
$$x_{32} = -85.2619330485231$$
$$x_{33} = -87.5256628989155$$
$$x_{34} = 71.8176996309665$$
$$x_{35} = 100.969896316472$$
$$x_{36} = -9.86370936236808$$
$$x_{37} = -47.5628212054456$$
$$x_{38} = 82.1203403949333$$
$$x_{39} = -62.3929216701972$$
$$x_{40} = -12.1274392127605$$
$$x_{41} = -28.7132652839068$$
$$x_{42} = -66.4123771269844$$
$$x_{43} = -3.5805240551885$$
$$x_{44} = 13.0053020159579$$
$$x_{45} = 6.72211670877829$$
$$x_{46} = 8.98584655917068$$
$$x_{47} = -30.9769951342992$$
$$x_{48} = -4435.48989546719$$
$$x_{49} = 27.8354024807094$$
$$x_{50} = 46.6849584022482$$
$$x_{51} = 38.1380432446762$$
$$x_{52} = 50.7044138590354$$
$$x_{53} = -97.8283036628823$$
$$x_{54} = -91.5451183557027$$
$$x_{55} = -18.4106245199401$$
$$x_{56} = 19.2884873231375$$
$$x_{57} = -106.375218820454$$
$$x_{58} = 52.9681437094278$$
$$x_{59} = 90.6672555525053$$
$$x_{60} = -43.5433657486584$$
$$x_{61} = -5.84425390558088$$
$$x_{62} = 40.4017730950686$$
$$x_{63} = 88.4035257021129$$
$$x_{64} = 15.2690318663503$$
$$x_{65} = 21.5522171735298$$
$$x_{66} = 94.6867110092925$$
$$x_{67} = -81.2424775917359$$
$$x_{68} = -93.8088482060951$$
$$x_{69} = 78.1008849381461$$
$$x_{70} = -100.092033513275$$
$$x_{71} = 75.8371550877537$$