El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(2 \sin{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - \frac{1}{3} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 2 \operatorname{atan}{\left(\frac{3}{4} + \frac{\sqrt{21}}{4} + \frac{\sqrt{2} \sqrt{7 + 3 \sqrt{21}}}{4} \right)}$$
$$x_{2} = 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{7 + 3 \sqrt{21}}}{4} + \frac{3}{4} + \frac{\sqrt{21}}{4} \right)}$$
Solución numérica$$x_{1} = -16.2636481188329$$
$$x_{2} = -37.1434269921935$$
$$x_{3} = -41.3963893475513$$
$$x_{4} = -47.6795746547309$$
$$x_{5} = -66.5291305762696$$
$$x_{6} = -79.0955011906288$$
$$x_{7} = -3.69727750447376$$
$$x_{8} = -91.661871804988$$
$$x_{9} = -137519.521133389$$
$$x_{10} = 0.555684850883971$$
$$x_{11} = 71.7009461816813$$
$$x_{12} = -137.674391907067$$
$$x_{13} = 44.5379820011411$$
$$x_{14} = -30.860241685014$$
$$x_{15} = 2.58590780270582$$
$$x_{16} = 101.086649765757$$
$$x_{17} = 77.9841314888609$$
$$x_{18} = -12.0106857634752$$
$$x_{19} = 90.55050210322$$
$$x_{20} = 21.4354637242446$$
$$x_{21} = 50.8211673083207$$
$$x_{22} = 84.2673167960404$$
$$x_{23} = -55.9929829137323$$
$$x_{24} = 19.4052407724227$$
$$x_{25} = 82.2370938442186$$
$$x_{26} = 75.953908537039$$
$$x_{27} = -72.8123158834492$$
$$x_{28} = -2613.24940293582$$
$$x_{29} = 38.2547966939615$$
$$x_{30} = -87.4089094496302$$
$$x_{31} = -99.9752800639894$$
$$x_{32} = 8.86909310988541$$
$$x_{33} = 13.1220554652431$$
$$x_{34} = -49.7097976065527$$
$$x_{35} = -62.2761682209119$$
$$x_{36} = 69.6707232298594$$
$$x_{37} = -43.4266122993731$$
$$x_{38} = 57.1043526155002$$
$$x_{39} = 25.6884260796023$$
$$x_{40} = -60.24594526909$$
$$x_{41} = 27.7186490314242$$
$$x_{42} = -9.98046281165335$$
$$x_{43} = -5.72750045629562$$
$$x_{44} = -53.9627599619105$$
$$x_{45} = 65.4177608745017$$
$$x_{46} = -81.1257241424507$$
$$x_{47} = -22.5468334260125$$
$$x_{48} = -9681.83287351286$$
$$x_{49} = -74.8425388352711$$
$$x_{50} = 34.0018343386038$$
$$x_{51} = 31.9716113867819$$
$$x_{52} = 6.83887015806356$$
$$x_{53} = 59.1345755673221$$
$$x_{54} = 63.3875379226798$$
$$x_{55} = -148.210539569604$$
$$x_{56} = -2016.34679875376$$
$$x_{57} = -18.2938710706548$$
$$x_{58} = -24.5770563778344$$
$$x_{59} = 94.8034644585778$$
$$x_{60} = 88.5202791513982$$
$$x_{61} = 46.5682049529629$$
$$x_{62} = 96.8336874103996$$
$$x_{63} = -97.9450571121676$$
$$x_{64} = 15.152278417065$$
$$x_{65} = -28.8300187331921$$
$$x_{66} = -35.1132040403717$$
$$x_{67} = -68.5593535280915$$
$$x_{68} = 52.8513902601425$$
$$x_{69} = 40.2850196457833$$
$$x_{70} = -93.6920947568098$$
$$x_{71} = -85.3786864978084$$