El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin^{3}{\left(4 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{4}$$
Solución numérica$$x_{1} = 2.35617114588618$$
$$x_{2} = -63.6172774911689$$
$$x_{3} = 94.2477801894507$$
$$x_{4} = -10.2101777105065$$
$$x_{5} = 95.8185986218888$$
$$x_{6} = 69.9004624021296$$
$$x_{7} = -89.5353813853192$$
$$x_{8} = 16.4933605711122$$
$$x_{9} = -73.827412061343$$
$$x_{10} = -19.6349786066294$$
$$x_{11} = 18.0641414851104$$
$$x_{12} = -99.7455679126634$$
$$x_{13} = -76.1835999943275$$
$$x_{14} = -65.9734545707223$$
$$x_{15} = -53.4070668003795$$
$$x_{16} = -3.92700729958738$$
$$x_{17} = -59.6902751688328$$
$$x_{18} = 6.28317678379747$$
$$x_{19} = 76.1836364522822$$
$$x_{20} = 51.8363056174327$$
$$x_{21} = 82.4668204774906$$
$$x_{22} = -91.8915942530772$$
$$x_{23} = 80.1106045607265$$
$$x_{24} = -25.9181553912765$$
$$x_{25} = -98.174745724584$$
$$x_{26} = 28.2743275768225$$
$$x_{27} = 84.0375915499608$$
$$x_{28} = 86.3937711718301$$
$$x_{29} = -85.6084265435726$$
$$x_{30} = -45.5531075780065$$
$$x_{31} = 32.2013365272205$$
$$x_{32} = 77.7544189342827$$
$$x_{33} = 14.1371739336473$$
$$x_{34} = 46.3384711445503$$
$$x_{35} = 91.891612011001$$
$$x_{36} = -43.9823031907204$$
$$x_{37} = 72.25662929658$$
$$x_{38} = 50.2654784195813$$
$$x_{39} = -32.2013146797895$$
$$x_{40} = 10.2101860894382$$
$$x_{41} = -84.0375911147445$$
$$x_{42} = -87.9646056659177$$
$$x_{43} = -23.5619647123173$$
$$x_{44} = 38.4845138201731$$
$$x_{45} = -69.900449061501$$
$$x_{46} = -95.8185611140798$$
$$x_{47} = -51.8362638128389$$
$$x_{48} = -62.0464399978641$$
$$x_{49} = 58.1194607741329$$
$$x_{50} = 21.9911516367321$$
$$x_{51} = -47.9093027046485$$
$$x_{52} = 20.420326944037$$
$$x_{53} = -40.055289069415$$
$$x_{54} = -77.7544170191301$$
$$x_{55} = 42.411474426101$$
$$x_{56} = -67.5442468859999$$
$$x_{57} = -29.8451166128144$$
$$x_{58} = 98.1747856701938$$
$$x_{59} = -11.7809645409866$$
$$x_{60} = 24.3473210693639$$
$$x_{61} = 54.192486686594$$
$$x_{62} = -54.1924559471174$$
$$x_{63} = 64.4026225609339$$
$$x_{64} = 40.0552909242107$$
$$x_{65} = 25.9181624777648$$
$$x_{66} = 65.9734546828098$$
$$x_{67} = -7.8539706790209$$
$$x_{68} = 90.3207716899113$$
$$x_{69} = -21.9911516353092$$
$$x_{70} = 36.1283175173302$$
$$x_{71} = -55.7632661383789$$
$$x_{72} = 87.964606010797$$
$$x_{73} = -33.7721152998264$$
$$x_{74} = 62.0464409714284$$
$$x_{75} = 0$$
$$x_{76} = -80.1105855543152$$
$$x_{77} = 43.9823032132585$$
$$x_{78} = 60.4756837175822$$
$$x_{79} = 33.7720993650945$$
$$x_{80} = -15.7079739460463$$
$$x_{81} = 68.329621355823$$
$$x_{82} = -81.6814256397462$$
$$x_{83} = 73.8274525867738$$
$$x_{84} = -18.0641383415282$$
$$x_{85} = 47.9093125551643$$
$$x_{86} = -1.57081959703317$$
$$x_{87} = -41.626128163397$$
$$x_{88} = -37.6991246006561$$
$$x_{89} = 3.92701217665881$$
$$x_{90} = 11.7809550697552$$
$$x_{91} = -76.9689934699144$$
$$x_{92} = -24.347331973333$$