El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$2 - 3 \sin{\left(x - \frac{\pi}{3} \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\pi}{6} + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
$$x_{2} = - \operatorname{acos}{\left(- \frac{2}{3} \right)} + \frac{11 \pi}{6}$$
Solución numérica$$x_{1} = 3.45906254855942$$
$$x_{2} = -65.655975830416$$
$$x_{3} = 89.7415195079378$$
$$x_{4} = 70.891963586399$$
$$x_{5} = -23.3558160212948$$
$$x_{6} = 14.3432958217827$$
$$x_{7} = 33.1928517433215$$
$$x_{8} = 2045.49428738193$$
$$x_{9} = 16.0254331629186$$
$$x_{10} = 64.6087782792194$$
$$x_{11} = -84.5055317519548$$
$$x_{12} = -21.6736786801589$$
$$x_{13} = 34.8749890844574$$
$$x_{14} = 39.4760370505011$$
$$x_{15} = -48.4885572500131$$
$$x_{16} = 58.3255929720398$$
$$x_{17} = 22.3086184700982$$
$$x_{18} = 45.7592223576807$$
$$x_{19} = 60.0077303131757$$
$$x_{20} = -59.3727905232364$$
$$x_{21} = -54.7717425571927$$
$$x_{22} = -27.9568639873385$$
$$x_{23} = 20.6264811289623$$
$$x_{24} = -15.3904933729793$$
$$x_{25} = -90.7887170591344$$
$$x_{26} = -2.82412275862016$$
$$x_{27} = 1.77692520742356$$
$$x_{28} = -53.0896052160569$$
$$x_{29} = 77.1751488935786$$
$$x_{30} = -35.922186635654$$
$$x_{31} = 1132.75028049975$$
$$x_{32} = -73.6212984787315$$
$$x_{33} = 72.5741009275349$$
$$x_{34} = 83.4583342007582$$
$$x_{35} = -42.2053719428335$$
$$x_{36} = 96.0247048151174$$
$$x_{37} = -71.9391611375956$$
$$x_{38} = -98.7540397074498$$
$$x_{39} = -78.2223464447752$$
$$x_{40} = 28.5918037772778$$
$$x_{41} = 78.8572862347145$$
$$x_{42} = 41.1581743916369$$
$$x_{43} = -79.9044837859111$$
$$x_{44} = 26.9096664361419$$
$$x_{45} = -92.4708544002702$$
$$x_{46} = 165.139743194093$$
$$x_{47} = -29.6390013284744$$
$$x_{48} = -46.8064199088773$$
$$x_{49} = 97.7068421562532$$
$$x_{50} = 53.7245450059961$$
$$x_{51} = -67.3381131715519$$
$$x_{52} = 66.2909156203553$$
$$x_{53} = 2007.79517553885$$
$$x_{54} = -4.50626009975602$$
$$x_{55} = 121.157446043836$$
$$x_{56} = -86.1876690930906$$
$$x_{57} = -61.0549278643723$$
$$x_{58} = -9.10730806579975$$
$$x_{59} = -268.400043001299$$
$$x_{60} = -40.5232346016977$$
$$x_{61} = 9.74224785573901$$
$$x_{62} = 47.4413596988165$$
$$x_{63} = 8.06011051460315$$
$$x_{64} = 85.140471541894$$
$$x_{65} = -34.2400492945181$$
$$x_{66} = 52.0424076648603$$
$$x_{67} = -10.7894454069356$$
$$x_{68} = 91.4236568490736$$
$$x_{69} = -97.071902366314$$
$$x_{70} = -17.0726307141152$$