El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\sin^{2}{\left(x \right)} - 3 \sin{\left(x \right)}\right) + 2 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{\pi}{2}$$
Solución numérica$$x_{1} = 1.57079536523077$$
$$x_{2} = 58.1194643770702$$
$$x_{3} = -29.8451289073854$$
$$x_{4} = -23.561945016053$$
$$x_{5} = 7.85398046563447$$
$$x_{6} = 83.2522046289214$$
$$x_{7} = -73.8274286445858$$
$$x_{8} = -61.2610571936019$$
$$x_{9} = 14.1371656591617$$
$$x_{10} = 20.4203521441984$$
$$x_{11} = 83.2522058456645$$
$$x_{12} = 95.8185771224127$$
$$x_{13} = -80.1106138557219$$
$$x_{14} = -67.5442421763137$$
$$x_{15} = 89.5353911752829$$
$$x_{16} = 76.9690207793905$$
$$x_{17} = -17.2787601164358$$
$$x_{18} = 51.8362776268483$$
$$x_{19} = 70.6858340517028$$
$$x_{20} = -17.2787586177095$$
$$x_{21} = 58.1194653976648$$
$$x_{22} = -73.8274260609448$$
$$x_{23} = -54.9778707171509$$
$$x_{24} = -80.1106125755117$$
$$x_{25} = 1.57079785005069$$
$$x_{26} = -23.561946075942$$
$$x_{27} = 70.6858357115182$$
$$x_{28} = -61.2610557825211$$
$$x_{29} = 89.5353909435736$$
$$x_{30} = 70.6858344445529$$
$$x_{31} = -29.8451300938139$$
$$x_{32} = -117.80972560988$$
$$x_{33} = 83.2522058481918$$
$$x_{34} = 32.9867236138576$$
$$x_{35} = -36.1283142806347$$
$$x_{36} = -92.676982808917$$
$$x_{37} = -4.71238848059836$$
$$x_{38} = 95.8185760701987$$
$$x_{39} = 45.553094091839$$
$$x_{40} = -48.6946868672216$$
$$x_{41} = -92.6769845303487$$
$$x_{42} = -73.8274272794653$$
$$x_{43} = -92.6769840326577$$
$$x_{44} = -23.5619437177603$$
$$x_{45} = 39.2699086837397$$
$$x_{46} = 1.57079661901596$$
$$x_{47} = 1.57079700398873$$
$$x_{48} = 64.4026493044641$$
$$x_{49} = -80.1106114181945$$
$$x_{50} = -86.3937977050157$$
$$x_{51} = -10.9955747752993$$
$$x_{52} = 89.5353896949152$$
$$x_{53} = 7.85398174770883$$
$$x_{54} = -61.2610570407565$$
$$x_{55} = 45.5530937812277$$
$$x_{56} = 58.1194628121746$$
$$x_{57} = -86.3937971842945$$
$$x_{58} = 39.2699074635758$$
$$x_{59} = 32.9867223887206$$
$$x_{60} = -17.2787598788452$$
$$x_{61} = -42.4115000881114$$
$$x_{62} = 20.4203510568788$$
$$x_{63} = -42.4115017994301$$
$$x_{64} = -36.1283166952282$$
$$x_{65} = -54.9778719394428$$
$$x_{66} = 14.1371682454946$$
$$x_{67} = -36.1283154137715$$
$$x_{68} = 14.1371671181822$$
$$x_{69} = -67.544243206816$$
$$x_{70} = 51.8362799897705$$
$$x_{71} = 102.101759965899$$
$$x_{72} = -10.9955735516589$$
$$x_{73} = -98.9601691037059$$
$$x_{74} = 95.8185747883961$$
$$x_{75} = 7.85398285538609$$
$$x_{76} = 26.703537282924$$
$$x_{77} = -325.154840065363$$
$$x_{78} = -29.8451314931042$$
$$x_{79} = 20.4203534431639$$
$$x_{80} = 45.5530925300164$$
$$x_{81} = 26.7035385469741$$
$$x_{82} = 64.4026481915252$$
$$x_{83} = 64.4026506037314$$
$$x_{84} = -4.71238970180774$$
$$x_{85} = -67.544240879025$$
$$x_{86} = 26.7035369653861$$
$$x_{87} = -42.4115005430641$$
$$x_{88} = 51.8362789090115$$
$$x_{89} = -48.6946856448184$$
$$x_{90} = -98.9601678826108$$
$$x_{91} = 76.9690195526133$$
$$x_{92} = -86.3937989639545$$