El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\frac{1}{\tan^{2}{\left(x \right)}} + \frac{3}{\sin{\left(x \right)}}\right) + 3 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{5 \pi}{6}$$
$$x_{2} = - \frac{\pi}{6}$$
Solución numérica$$x_{1} = 62.3082542961976$$
$$x_{2} = 23.5619453078933$$
$$x_{3} = -58.1194639979337$$
$$x_{4} = -3732.73567124027$$
$$x_{5} = -34.0339204138894$$
$$x_{6} = 92.6769830424575$$
$$x_{7} = -31.9395253114962$$
$$x_{8} = 48.6946859212927$$
$$x_{9} = -83.2522055331946$$
$$x_{10} = 93.7241808320955$$
$$x_{11} = 18.3259571459405$$
$$x_{12} = 67.5442422767088$$
$$x_{13} = -130038.37391261$$
$$x_{14} = -64.4026491822289$$
$$x_{15} = -51.8362786893433$$
$$x_{16} = -27.7507351067098$$
$$x_{17} = -20.4203517364181$$
$$x_{18} = 49.7418836818384$$
$$x_{19} = -7.85398149693444$$
$$x_{20} = 92.6769830753239$$
$$x_{21} = 61.2610568360414$$
$$x_{22} = 54.9778708425296$$
$$x_{23} = -76.969018918312$$
$$x_{24} = 100.007366139275$$
$$x_{25} = -96.8657734856853$$
$$x_{26} = 73.8274274823479$$
$$x_{27} = 24.60914245312$$
$$x_{28} = -8.90117918517108$$
$$x_{29} = -39.2699083833206$$
$$x_{30} = -14.1371668374498$$
$$x_{31} = -20.4203521145122$$
$$x_{32} = -65.4498469497874$$
$$x_{33} = 80.1106117802993$$
$$x_{34} = -71.733032256967$$
$$x_{35} = -89.5353907494205$$
$$x_{36} = 22.5147473507269$$
$$x_{37} = -78.0162175641465$$
$$x_{38} = 4.71238876831369$$
$$x_{39} = 23.5619451247945$$
$$x_{40} = -20.4203525724933$$
$$x_{41} = 86.3937978871775$$
$$x_{42} = 16.2315620435473$$
$$x_{43} = 4.71238848803862$$
$$x_{44} = -1.57079643148837$$
$$x_{45} = 111.526537725933$$
$$x_{46} = -75.9218224617533$$
$$x_{47} = -82.2050077689329$$
$$x_{48} = 60.2138591938044$$
$$x_{49} = 66.497044500984$$
$$x_{50} = -20.4203520282497$$
$$x_{51} = 48.6946856349272$$
$$x_{52} = -95.8185761068952$$
$$x_{53} = 29.8451303226255$$
$$x_{54} = 67.5442426433204$$
$$x_{55} = -21.4675497995303$$
$$x_{56} = -38.2227106186758$$
$$x_{57} = -95.8185758680487$$
$$x_{58} = 12.0427718387609$$
$$x_{59} = 35.081117965086$$
$$x_{60} = -25.6563400043166$$
$$x_{61} = 36.1283157588508$$
$$x_{62} = 80.1106131429919$$
$$x_{63} = 5.75958653158129$$
$$x_{64} = -64.4026495447916$$
$$x_{65} = 42.4115007277485$$
$$x_{66} = 3.66519142918809$$
$$x_{67} = 80.1106124822091$$
$$x_{68} = -64.4026494478211$$
$$x_{69} = 10.9955739339028$$
$$x_{70} = -46.6002910282486$$
$$x_{71} = -7.85398093365523$$
$$x_{72} = 212.057503824382$$
$$x_{73} = -40.317105721069$$
$$x_{74} = 56.025068989018$$
$$x_{75} = -45.5530935905433$$
$$x_{76} = 48.6946858079193$$
$$x_{77} = 85.3466004225227$$
$$x_{78} = 10.9955744676559$$