El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin^{2}{\left(x \right)} + \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - 2 \operatorname{atan}{\left(\sqrt{2 + \sqrt{5}} \right)}$$
$$x_{2} = 2 \operatorname{atan}{\left(\sqrt{2 + \sqrt{5}} \right)}$$
Solución numérica$$x_{1} = 71.3520741382629$$
$$x_{2} = -16.6125201622513$$
$$x_{3} = -46.2193329095445$$
$$x_{4} = 46.2193329095445$$
$$x_{5} = 16.6125201622513$$
$$x_{6} = -71.3520741382629$$
$$x_{7} = 90.2016300598016$$
$$x_{8} = 58.7857035239037$$
$$x_{9} = 85.7275585412268$$
$$x_{10} = 22.8957054694309$$
$$x_{11} = -33.6529622951853$$
$$x_{12} = 8.520221066467$$
$$x_{13} = -4.04614954789217$$
$$x_{14} = 66.878002619688$$
$$x_{15} = -96.4848153669812$$
$$x_{16} = 29.1788907766105$$
$$x_{17} = -27.3697769880058$$
$$x_{18} = -79.4443732340472$$
$$x_{19} = -77.6352594454424$$
$$x_{20} = 52.5025182167241$$
$$x_{21} = -442.060007261858$$
$$x_{22} = 2.23703575928741$$
$$x_{23} = 4.04614954789217$$
$$x_{24} = 65.0688888310833$$
$$x_{25} = -39.9361476023649$$
$$x_{26} = -35.4620760837901$$
$$x_{27} = -60.5948173125085$$
$$x_{28} = 92.0107438484064$$
$$x_{29} = -73.1611879268676$$
$$x_{30} = 21.0865916808262$$
$$x_{31} = 83.918444752622$$
$$x_{32} = -48.0284466981493$$
$$x_{33} = 98.293929155586$$
$$x_{34} = 35.4620760837901$$
$$x_{35} = -98.293929155586$$
$$x_{36} = -8.520221066467$$
$$x_{37} = -29.1788907766105$$
$$x_{38} = 48.0284466981493$$
$$x_{39} = -92.0107438484064$$
$$x_{40} = 79.4443732340472$$
$$x_{41} = -52.5025182167241$$
$$x_{42} = -22.8957054694309$$
$$x_{43} = 77.6352594454424$$
$$x_{44} = -14.8034063736466$$
$$x_{45} = 41.7452613909697$$
$$x_{46} = 73.1611879268676$$
$$x_{47} = 54.3116320053289$$
$$x_{48} = 60.5948173125085$$
$$x_{49} = 96.4848153669812$$
$$x_{50} = 27.3697769880058$$
$$x_{51} = -90.2016300598016$$
$$x_{52} = 102.768000674161$$
$$x_{53} = -10.3293348550718$$
$$x_{54} = -2.23703575928741$$
$$x_{55} = -41.7452613909697$$
$$x_{56} = -102.768000674161$$
$$x_{57} = 39.9361476023649$$
$$x_{58} = 10.3293348550718$$
$$x_{59} = -66.878002619688$$
$$x_{60} = -83.918444752622$$
$$x_{61} = -85.7275585412268$$
$$x_{62} = 33.6529622951853$$
$$x_{63} = -58.7857035239037$$
$$x_{64} = 14.8034063736466$$
$$x_{65} = -54.3116320053289$$