El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(2 x \right)} - \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{5 \pi}{6}$$
Solución numérica$$x_{1} = -64.4026493985908$$
$$x_{2} = -12.0427718387609$$
$$x_{3} = -23.5619449019235$$
$$x_{4} = 44.5058959258554$$
$$x_{5} = -29.845130209103$$
$$x_{6} = 42.4115008234622$$
$$x_{7} = 4.71238898038469$$
$$x_{8} = -22.5147473507269$$
$$x_{9} = 36.1283155162826$$
$$x_{10} = 34.0339204138894$$
$$x_{11} = 23.5619449019235$$
$$x_{12} = -17.2787595947439$$
$$x_{13} = -5.75958653158129$$
$$x_{14} = 65.4498469497874$$
$$x_{15} = -80.1106126665397$$
$$x_{16} = 86.3937979737193$$
$$x_{17} = 64.4026493985908$$
$$x_{18} = -83.2522053201295$$
$$x_{19} = -95.8185759344887$$
$$x_{20} = 50.789081233035$$
$$x_{21} = -1.5707963267949$$
$$x_{22} = 71.733032256967$$
$$x_{23} = -60.2138591938044$$
$$x_{24} = -81.1578102177363$$
$$x_{25} = -72.7802298081635$$
$$x_{26} = 73.8274273593601$$
$$x_{27} = 31.9395253114962$$
$$x_{28} = -39.2699081698724$$
$$x_{29} = 67.5442420521806$$
$$x_{30} = 78.0162175641465$$
$$x_{31} = 84.2994028713261$$
$$x_{32} = -93.7241808320955$$
$$x_{33} = -3.66519142918809$$
$$x_{34} = -66.497044500984$$
$$x_{35} = -42.4115008234622$$
$$x_{36} = -56.025068989018$$
$$x_{37} = -51.8362787842316$$
$$x_{38} = 58.1194640914112$$
$$x_{39} = -87.4409955249159$$
$$x_{40} = -73.8274273593601$$
$$x_{41} = 51.8362787842316$$
$$x_{42} = 29.845130209103$$
$$x_{43} = 27.7507351067098$$
$$x_{44} = -45.553093477052$$
$$x_{45} = 75.9218224617533$$
$$x_{46} = 102.101761241668$$
$$x_{47} = 80.1106126665397$$
$$x_{48} = -58.1194640914112$$
$$x_{49} = -49.7418836818384$$
$$x_{50} = -36.1283155162826$$
$$x_{51} = -100.007366139275$$
$$x_{52} = -9.94837673636768$$
$$x_{53} = -97.9129710368819$$
$$x_{54} = 38.2227106186758$$
$$x_{55} = -67.5442420521806$$
$$x_{56} = 0.523598775598299$$
$$x_{57} = -43.4586983746588$$
$$x_{58} = -7.85398163397448$$
$$x_{59} = 48.6946861306418$$
$$x_{60} = 82.2050077689329$$
$$x_{61} = 7.85398163397448$$
$$x_{62} = -14.1371669411541$$
$$x_{63} = -53.9306738866248$$
$$x_{64} = -2937.91272988205$$
$$x_{65} = -4.71238898038469$$
$$x_{66} = -91.6297857297023$$
$$x_{67} = 14.1371669411541$$
$$x_{68} = -16.2315620435473$$
$$x_{69} = 57.0722665402146$$
$$x_{70} = 40.317105721069$$
$$x_{71} = -37.1755130674792$$
$$x_{72} = 20.4203522483337$$
$$x_{73} = 95.8185759344887$$
$$x_{74} = -89.5353906273091$$
$$x_{75} = -47.6474885794452$$
$$x_{76} = 6.80678408277789$$
$$x_{77} = 92.6769832808989$$
$$x_{78} = 94.7713783832921$$
$$x_{79} = 88.4881930761125$$
$$x_{80} = 21.4675497995303$$
$$x_{81} = -20.4203522483337$$