El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\sin{\left(4 x \right)} \cot{\left(2 x \right)} - \cos{\left(4 x \right)}\right) - \sin{\left(3 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{\pi}{6}$$
Solución numérica$$x_{1} = -64.4026492298162$$
$$x_{2} = -22.5147471967799$$
$$x_{3} = 80.1106131528868$$
$$x_{4} = 48.6946859683928$$
$$x_{5} = -68.5914394976747$$
$$x_{6} = 31.9395253654771$$
$$x_{7} = 78.0162175420896$$
$$x_{8} = -43.458698513903$$
$$x_{9} = -79.0634150011636$$
$$x_{10} = -7.85398150192478$$
$$x_{11} = -70.6858348165339$$
$$x_{12} = 21.4675499464553$$
$$x_{13} = 94.7713782337162$$
$$x_{14} = -60.2138590635982$$
$$x_{15} = 23.5619450702353$$
$$x_{16} = -93.7241808501502$$
$$x_{17} = 73.8274274735132$$
$$x_{18} = 38.2227106406479$$
$$x_{19} = -39.2699083292704$$
$$x_{20} = -16.2315619072654$$
$$x_{21} = -85.3466005833809$$
$$x_{22} = -66.4970445282258$$
$$x_{23} = -83.252205476317$$
$$x_{24} = -62.308254139164$$
$$x_{25} = -3.66519148254904$$
$$x_{26} = -24.6091423681141$$
$$x_{27} = -66.4970443416682$$
$$x_{28} = 25.6563401677065$$
$$x_{29} = 27.7507352485908$$
$$x_{30} = 44.5058957975625$$
$$x_{31} = -58.1194640021532$$
$$x_{32} = 17.2787592807644$$
$$x_{33} = -81.1578103224548$$
$$x_{34} = -87.4409956689738$$
$$x_{35} = 4.71238881902407$$
$$x_{36} = -12.0427717978327$$
$$x_{37} = 90.5825880287766$$
$$x_{38} = 86.3937978904858$$
$$x_{39} = -53.9306741017977$$
$$x_{40} = -49.7418836877459$$
$$x_{41} = -37.1755131881972$$
$$x_{42} = 75.9218225274375$$
$$x_{43} = 71.733032403968$$
$$x_{44} = 96.865773409958$$
$$x_{45} = -26.7035377567181$$
$$x_{46} = -100.007366130834$$
$$x_{47} = 69.6386373203027$$
$$x_{48} = 98.9601688300381$$
$$x_{49} = -47.6474886422567$$
$$x_{50} = -37.1755131460154$$
$$x_{51} = -41.3643034312689$$
$$x_{52} = -56.0250689629876$$
$$x_{53} = 50.789081090574$$
$$x_{54} = -45.5530935835137$$
$$x_{55} = 88.4881929539175$$
$$x_{56} = -5.75958652427337$$
$$x_{57} = 10.9955746928717$$
$$x_{58} = 2.61799372149593$$
$$x_{59} = -95.8185758682622$$
$$x_{60} = -91.6297858015358$$
$$x_{61} = 52.8834762893477$$
$$x_{62} = -85.3466004035061$$
$$x_{63} = 82.2050078076434$$
$$x_{64} = -35.081117920222$$
$$x_{65} = 54.977871797926$$
$$x_{66} = 61.2610563291673$$
$$x_{67} = -18.3259569854581$$
$$x_{68} = 63.3554518703442$$
$$x_{69} = 67.5442422190054$$
$$x_{70} = -9.94837684428868$$
$$x_{71} = -1.57079642588424$$
$$x_{72} = 65.4498470876666$$
$$x_{73} = 19.3731547552869$$
$$x_{74} = 6.8067839497432$$
$$x_{75} = 84.2994028383437$$
$$x_{76} = 29.845130315527$$
$$x_{77} = 40.31710567763$$
$$x_{78} = -3.66519119284134$$
$$x_{79} = -28.7979326032841$$
$$x_{80} = 46.6002908748595$$
$$x_{81} = 34.0339203588006$$
$$x_{82} = 92.6769831186997$$
$$x_{83} = -14.1371668430111$$
$$x_{84} = -51.8362786904677$$
$$x_{85} = -20.4203520794005$$
$$x_{86} = 42.411500732115$$
$$x_{87} = 8.90117917814493$$
$$x_{88} = -89.5353907407704$$