El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(4 x \right)} + \cos{\left(3 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = - \frac{\pi}{14}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{11 \pi}{14}$$
$$x_{5} = - i \log{\left(- \sqrt[14]{-1} \right)}$$
Solución numérica$$x_{1} = 54.5290724873086$$
$$x_{2} = -76.5202210624371$$
$$x_{3} = -7.85398163397448$$
$$x_{4} = -58.1194640914112$$
$$x_{5} = 66.1978452006421$$
$$x_{6} = 82.3546074191039$$
$$x_{7} = 41.9627018729494$$
$$x_{8} = -15.4835637926926$$
$$x_{9} = 64.4026493985908$$
$$x_{10} = 15.9323627432054$$
$$x_{11} = 30.2939291596159$$
$$x_{12} = -29.845130209103$$
$$x_{13} = 87.7401948252578$$
$$x_{14} = 12.3419711391028$$
$$x_{15} = -88.1889937757706$$
$$x_{16} = -5.60998688141034$$
$$x_{17} = 85.9449990232065$$
$$x_{18} = -41.5139029224366$$
$$x_{19} = -32.9867228626928$$
$$x_{20} = -47.7970882296161$$
$$x_{21} = 95.8185759344887$$
$$x_{22} = -81.905808468591$$
$$x_{23} = 58.1194640914112$$
$$x_{24} = 22.215548050385$$
$$x_{25} = -73.8274273593601$$
$$x_{26} = -49.5922840316675$$
$$x_{27} = 7.85398163397448$$
$$x_{28} = -2.01959527730772$$
$$x_{29} = 72.4810305078217$$
$$x_{30} = 24.0107438524363$$
$$x_{31} = -21.7667490998721$$
$$x_{32} = -75.6226231614115$$
$$x_{33} = 50.0410829821803$$
$$x_{34} = -98.0625706870528$$
$$x_{35} = -67.5442420521806$$
$$x_{36} = 10.9955742875643$$
$$x_{37} = 4.26359002987186$$
$$x_{38} = 20.4203522483337$$
$$x_{39} = 46.4506913780777$$
$$x_{40} = -89.9841895778219$$
$$x_{41} = 67.9930410026934$$
$$x_{42} = 77.8666179139756$$
$$x_{43} = 98.5113696375657$$
$$x_{44} = 48.245887180129$$
$$x_{45} = -55.875469338847$$
$$x_{46} = -39.7187071203852$$
$$x_{47} = 90.4329885283348$$
$$x_{48} = -58.568263041924$$
$$x_{49} = 28.4987333575646$$
$$x_{50} = -99.8577664891041$$
$$x_{51} = -65.7490462501292$$
$$x_{52} = -72.0322315573088$$
$$x_{53} = -3.81479107935903$$
$$x_{54} = -0.224399475256414$$
$$x_{55} = 80.1106126665397$$
$$x_{56} = 43.7578976750007$$
$$x_{57} = -13.6883679906412$$
$$x_{58} = -46.0018924275648$$
$$x_{59} = 25.8059396544876$$
$$x_{60} = 32.0891249616672$$
$$x_{61} = -18.1763574957695$$
$$x_{62} = 2.46839422782055$$
$$x_{63} = -28.0499344070517$$
$$x_{64} = -10.0979763865386$$
$$x_{65} = -95.8185759344887$$
$$x_{66} = -36.1283155162826$$
$$x_{67} = -91.7793853798732$$
$$x_{68} = 33.8843207637185$$
$$x_{69} = 51.8362787842316$$
$$x_{70} = -31.6403260111543$$
$$x_{71} = 56.3242682893599$$
$$x_{72} = 69.7882368047447$$
$$x_{73} = -54.0802735367957$$
$$x_{74} = 40.1675060708981$$
$$x_{75} = -83.7010042706423$$
$$x_{76} = 6.05878583192317$$
$$x_{77} = -63.9538504480779$$
$$x_{78} = 74.276226309873$$
$$x_{79} = -93.5745811819246$$
$$x_{80} = 38.3723102688468$$
$$x_{81} = -83.2522053201295$$
$$x_{82} = 100.306565439617$$
$$x_{83} = -26.2547386050004$$
$$x_{84} = 17.7275585452567$$
$$x_{85} = 76.0714221119243$$
$$x_{86} = -51.8362787842316$$
$$x_{87} = -19.9715532978208$$
$$x_{88} = -11.8931721885899$$
$$x_{89} = 36.1283155162826$$
$$x_{90} = 84.1498032211552$$
$$x_{91} = 94.0233801324374$$
$$x_{92} = -23.5619449019235$$
$$x_{93} = -62.1586546460266$$
$$x_{94} = 92.2281843303861$$
$$x_{95} = -70.2370357552575$$
$$x_{96} = -37.9235113183339$$
$$x_{97} = 14.1371669411541$$
$$x_{98} = 59.9146598934625$$
$$x_{99} = -80.1106126665397$$
$$x_{100} = -44.2066966255135$$