El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(2 \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) - 2 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{2 \pi}{3}$$
$$x_{2} = - \frac{\pi}{2}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{2 \pi}{3}$$
Solución numérica$$x_{1} = 98.4365698124802$$
$$x_{2} = -71.2094334813686$$
$$x_{3} = 96.342174710087$$
$$x_{4} = -92.1533845053006$$
$$x_{5} = -83.7758040957278$$
$$x_{6} = -98.9601685880785$$
$$x_{7} = -111.002940426839$$
$$x_{8} = -48.1710873550435$$
$$x_{9} = -64.4026493985908$$
$$x_{10} = 16.7551608191456$$
$$x_{11} = 73.8274273593601$$
$$x_{12} = -23.0383461263252$$
$$x_{13} = 89.5353906273091$$
$$x_{14} = 76.9690200129499$$
$$x_{15} = 8.37758040957278$$
$$x_{16} = -2.0943951023932$$
$$x_{17} = -58.1194640914112$$
$$x_{18} = -81877.758534184$$
$$x_{19} = 41.8879020478639$$
$$x_{20} = -61.261056745001$$
$$x_{21} = -51.8362787842316$$
$$x_{22} = -39.7935069454707$$
$$x_{23} = -86.3937979737193$$
$$x_{24} = 58.1194640914112$$
$$x_{25} = 23.5619449019235$$
$$x_{26} = -67.5442420521806$$
$$x_{27} = -41.8879020478639$$
$$x_{28} = -35.6047167406843$$
$$x_{29} = -10.471975511966$$
$$x_{30} = -67.0206432765823$$
$$x_{31} = 39.7935069454707$$
$$x_{32} = 48.1710873550435$$
$$x_{33} = -70.6858347057703$$
$$x_{34} = -77.4926187885482$$
$$x_{35} = -95.8185759344887$$
$$x_{36} = -27.2271363311115$$
$$x_{37} = -1072.33029242532$$
$$x_{38} = 29.845130209103$$
$$x_{39} = 80.1106126665397$$
$$x_{40} = 54.9778714378214$$
$$x_{41} = -76.9690200129499$$
$$x_{42} = 61.261056745001$$
$$x_{43} = -54.4542726622231$$
$$x_{44} = 52.3598775598299$$
$$x_{45} = -29.845130209103$$
$$x_{46} = 85.870199198121$$
$$x_{47} = -20.4203522483337$$
$$x_{48} = -33.5103216382911$$
$$x_{49} = 33.5103216382911$$
$$x_{50} = 92.1533845053006$$
$$x_{51} = -17.2787595947439$$
$$x_{52} = 20.4203522483337$$
$$x_{53} = 67.5442420521806$$
$$x_{54} = 14.1371669411541$$
$$x_{55} = -26.7035375555132$$
$$x_{56} = 2.0943951023932$$
$$x_{57} = 4.71238898038469$$
$$x_{58} = 70.6858347057703$$
$$x_{59} = 83.7758040957278$$
$$x_{60} = 10.471975511966$$
$$x_{61} = 32.9867228626928$$
$$x_{62} = -23.5619449019235$$
$$x_{63} = -90.0589894029074$$
$$x_{64} = 77.4926187885482$$
$$x_{65} = 54.4542726622231$$
$$x_{66} = 36.1283155162826$$
$$x_{67} = 46.0766922526503$$
$$x_{68} = 17.2787595947439$$
$$x_{69} = 10.9955742875643$$
$$x_{70} = 4.18879020478639$$
$$x_{71} = -14.1371669411541$$
$$x_{72} = -46.0766922526503$$
$$x_{73} = -4.71238898038469$$
$$x_{74} = 83.2522053201295$$
$$x_{75} = 98.9601685880785$$
$$x_{76} = 26.7035375555132$$
$$x_{77} = -85.870199198121$$
$$x_{78} = 60.7374579694027$$
$$x_{79} = 20.943951023932$$
$$x_{80} = -32.9867228626928$$
$$x_{81} = 39.2699081698724$$
$$x_{82} = -7.85398163397448$$
$$x_{83} = 64.4026493985908$$
$$x_{84} = 90.0589894029074$$
$$x_{85} = -10.9955742875643$$
$$x_{86} = -98.4365698124802$$
$$x_{87} = -73.8274273593601$$
$$x_{88} = -54.9778714378214$$
$$x_{89} = -4.18879020478639$$
$$x_{90} = -42.4115008234622$$