El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(2 x \right)} + 2 \cdot 8 \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{2}$$
Solución numérica$$x_{1} = 7.85398163397448$$
$$x_{2} = -73.8274273593601$$
$$x_{3} = -54.9778714378214$$
$$x_{4} = 73.8274273593601$$
$$x_{5} = -26.7035375555132$$
$$x_{6} = -1.5707963267949$$
$$x_{7} = -95.8185759344887$$
$$x_{8} = -39.2699081698724$$
$$x_{9} = -4.71238898038469$$
$$x_{10} = 14.1371669411541$$
$$x_{11} = -152.367243699105$$
$$x_{12} = 10.9955742875643$$
$$x_{13} = 58.1194640914112$$
$$x_{14} = 70.6858347057703$$
$$x_{15} = -36.1283155162826$$
$$x_{16} = 54.9778714378214$$
$$x_{17} = 23.5619449019235$$
$$x_{18} = 111.526539202438$$
$$x_{19} = 724.137106652447$$
$$x_{20} = -92.6769832808989$$
$$x_{21} = 651.880475619882$$
$$x_{22} = -86.3937979737193$$
$$x_{23} = -10.9955742875643$$
$$x_{24} = -32.9867228626928$$
$$x_{25} = 39.2699081698724$$
$$x_{26} = 15558.7376169035$$
$$x_{27} = 92.6769832808989$$
$$x_{28} = 98.9601685880785$$
$$x_{29} = 36.1283155162826$$
$$x_{30} = -7.85398163397448$$
$$x_{31} = -58.1194640914112$$
$$x_{32} = -67.5442420521806$$
$$x_{33} = -61.261056745001$$
$$x_{34} = 26.7035375555132$$
$$x_{35} = 86.3937979737193$$
$$x_{36} = -48.6946861306418$$
$$x_{37} = 51.8362787842316$$
$$x_{38} = -42.4115008234622$$
$$x_{39} = -89.5353906273091$$
$$x_{40} = -98.9601685880785$$
$$x_{41} = -14.1371669411541$$
$$x_{42} = -64.4026493985908$$
$$x_{43} = 80.1106126665397$$
$$x_{44} = 95.8185759344887$$
$$x_{45} = 1.5707963267949$$
$$x_{46} = 45.553093477052$$
$$x_{47} = -17.2787595947439$$
$$x_{48} = 4.71238898038469$$
$$x_{49} = 48.6946861306418$$
$$x_{50} = 76.9690200129499$$
$$x_{51} = -45.553093477052$$
$$x_{52} = 20.4203522483337$$
$$x_{53} = 17.2787595947439$$
$$x_{54} = -83.2522053201295$$
$$x_{55} = -20.4203522483337$$
$$x_{56} = -80.1106126665397$$
$$x_{57} = 61.261056745001$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 64.4026493985908$$
$$x_{60} = -23.5619449019235$$
$$x_{61} = 29.845130209103$$
$$x_{62} = 42.4115008234622$$
$$x_{63} = 89.5353906273091$$
$$x_{64} = -51.8362787842316$$
$$x_{65} = -70.6858347057703$$
$$x_{66} = 83.2522053201295$$
$$x_{67} = 67.5442420521806$$
$$x_{68} = -29.845130209103$$
$$x_{69} = 2574.53517961684$$
$$x_{70} = -76.9690200129499$$