El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin^{6}{\left(x \right)} \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 0$$
$$x_{2} = - \frac{\pi}{2}$$
$$x_{3} = \frac{\pi}{2}$$
Solución numérica$$x_{1} = 72.2564681995667$$
$$x_{2} = -21.9913952130885$$
$$x_{3} = 7.85398163397448$$
$$x_{4} = 15.7155274169849$$
$$x_{5} = 34.5503466421936$$
$$x_{6} = 87.9655804270211$$
$$x_{7} = -65.9741855218327$$
$$x_{8} = 58.1194640914112$$
$$x_{9} = -81.6830903260566$$
$$x_{10} = 12.5590139806329$$
$$x_{11} = -6.27581837004495$$
$$x_{12} = -43.9827903906253$$
$$x_{13} = 28.2737364436143$$
$$x_{14} = 94.2478341327998$$
$$x_{15} = 0$$
$$x_{16} = -29.845130209103$$
$$x_{17} = 81.6895496856672$$
$$x_{18} = 86.3937979737193$$
$$x_{19} = 21.9913952130384$$
$$x_{20} = -31.4236461391621$$
$$x_{21} = -15.7089949109591$$
$$x_{22} = 20.4203522483337$$
$$x_{23} = -72.2498706463197$$
$$x_{24} = -75.4062991299145$$
$$x_{25} = 14.1371669411541$$
$$x_{26} = 42.4115008234622$$
$$x_{27} = 78.5330170231139$$
$$x_{28} = 73.8274273593601$$
$$x_{29} = -37.7003603220942$$
$$x_{30} = -7.85398163397448$$
$$x_{31} = -65.9811894209038$$
$$x_{32} = -95.8185759344887$$
$$x_{33} = 50.2651022915147$$
$$x_{34} = -23.5619449019235$$
$$x_{35} = -87.9655807165942$$
$$x_{36} = 64.4026493985908$$
$$x_{37} = -97.397622880584$$
$$x_{38} = -36.1283155162826$$
$$x_{39} = -1.5707963267949$$
$$x_{40} = -58.1194640914112$$
$$x_{41} = -53.4149735399443$$
$$x_{42} = 59.698211455972$$
$$x_{43} = -73.8274273593601$$
$$x_{44} = 29.845130209103$$
$$x_{45} = -94.2412263246354$$
$$x_{46} = 80.1106126665397$$
$$x_{47} = 43.9827903871798$$
$$x_{48} = 65.9741854777245$$
$$x_{49} = 6.28237069462517$$
$$x_{50} = 37.7068706961535$$
$$x_{51} = -9.432316956092$$
$$x_{52} = 56.5416809995023$$
$$x_{53} = 36.1283155162826$$
$$x_{54} = 100.524354683131$$
$$x_{55} = -28.267166652441$$
$$x_{56} = -50.2585174163754$$
$$x_{57} = -51.8362787842316$$
$$x_{58} = -80.1106126665397$$
$$x_{59} = -59.6917254813975$$
$$x_{60} = 51.8362787842316$$
$$x_{61} = 95.8185759344887$$
$$x_{62} = -14.1371669411541$$