El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\left(\sin{\left(x \right)} \cos{\left(3 x \right)} + 1\right) + 5 \sin{\left(2 x \right)}\right) - \sin{\left(3 x \right)} \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{i \left(\log{\left(4 \right)} - \log{\left(- \sqrt{15} - i \right)}\right)}{2}$$
$$x_{2} = \frac{i \left(\log{\left(4 \right)} - \log{\left(\sqrt{15} - i \right)}\right)}{2}$$
$$x_{3} = - i \log{\left(- \frac{\sqrt{- \sqrt{15} - i}}{2} \right)}$$
$$x_{4} = - i \log{\left(- \frac{\sqrt{\sqrt{15} - i}}{2} \right)}$$
Solución numérica$$x_{1} = 12.4400304867881$$
$$x_{2} = 50.1391423298656$$
$$x_{3} = -44.1086372778281$$
$$x_{4} = 80.2369527941108$$
$$x_{5} = -42.2851606958912$$
$$x_{6} = -97.5157123888546$$
$$x_{7} = -59.8166005457771$$
$$x_{8} = -84.9493417744955$$
$$x_{9} = -20.2940121207626$$
$$x_{10} = 48.8210262582128$$
$$x_{11} = -28.4006740098792$$
$$x_{12} = 58.2458042189822$$
$$x_{13} = 95.9449160620597$$
$$x_{14} = 43.8559570226861$$
$$x_{15} = 94.1214394801228$$
$$x_{16} = 20.5466923759047$$
$$x_{17} = 72.1302909049942$$
$$x_{18} = 37.5727717155065$$
$$x_{19} = 29.9714703366741$$
$$x_{20} = -45.426753349481$$
$$x_{21} = 1.69713645436594$$
$$x_{22} = 65.8471055978146$$
$$x_{23} = -29.718790081532$$
$$x_{24} = -79.9842725389687$$
$$x_{25} = 78.4134762121738$$
$$x_{26} = -94.3741197352648$$
$$x_{27} = -31.542266663469$$
$$x_{28} = 42.5378409510332$$
$$x_{29} = 56.4223276370452$$
$$x_{30} = 4.83872910795573$$
$$x_{31} = 51.9626189118026$$
$$x_{32} = -89.4090504997381$$
$$x_{33} = 36.2546556438537$$
$$x_{34} = 34.4311790619167$$
$$x_{35} = 67.6705821797516$$
$$x_{36} = 28.1479937547371$$
$$x_{37} = 100.404624787302$$
$$x_{38} = 92.8033234084699$$
$$x_{39} = 87.8382541729432$$
$$x_{40} = -14.010826813583$$
$$x_{41} = -67.4179019246095$$
$$x_{42} = 73.9537674869312$$
$$x_{43} = 6.15684517960855$$
$$x_{44} = -17.1524194671728$$
$$x_{45} = -64.2763092710197$$
$$x_{46} = -37.8254519706486$$
$$x_{47} = -88.0909344280852$$
$$x_{48} = 23.6882850294945$$
$$x_{49} = 64.5289895261618$$
$$x_{50} = 89.6617307548802$$
$$x_{51} = 21.8648084475575$$
$$x_{52} = 86.5201381012904$$
$$x_{53} = -15.83430339552$$
$$x_{54} = -103.798897696034$$
$$x_{55} = -81.8077491209057$$
$$x_{56} = -57.9931239638401$$
$$x_{57} = 59.563920290635$$
$$x_{58} = -50.3918225850077$$
$$x_{59} = 7.98032176154552$$
$$x_{60} = -78.6661564673159$$
$$x_{61} = -34.6838593170588$$
$$x_{62} = -53.5334152385975$$
$$x_{63} = 70.8121748333414$$
$$x_{64} = -9.55111808834042$$
$$x_{65} = -86.2674578461483$$
$$x_{66} = -95.6922358069177$$
$$x_{67} = -22.1174887026996$$
$$x_{68} = -6.40952543475063$$
$$x_{69} = 14.2635070687251$$
$$x_{70} = -1.44445619922386$$
$$x_{71} = -0.126340127571039$$
$$x_{72} = -7.72764150640344$$
$$x_{73} = -145.957718264354$$
$$x_{74} = -36.0019753887116$$
$$x_{75} = 81.5550688657636$$
$$x_{76} = -66.0997858529567$$
$$x_{77} = -51.7099386566605$$
$$x_{78} = 45.679433604623$$
$$x_{79} = -73.7010872317891$$
$$x_{80} = 26.8298776830843$$
$$x_{81} = -23.4356047743524$$
$$x_{82} = -72.3829711601363$$
$$x_{83} = 1757.84742981106$$
$$x_{84} = 15.5816231403779$$
$$x_{85} = -75.5245638137261$$