El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(5 x \right)} + \cos{\left(2 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{5 \pi}{6}$$
$$x_{2} = - \frac{\pi}{6}$$
$$x_{3} = - \frac{\pi}{14}$$
$$x_{4} = \frac{\pi}{2}$$
$$x_{5} = \frac{11 \pi}{14}$$
$$x_{6} = - i \log{\left(- \sqrt[14]{-1} \right)}$$
Solución numérica$$x_{1} = 33.8843207637185$$
$$x_{2} = -71.733032256967$$
$$x_{3} = -28.0499344070517$$
$$x_{4} = 20.4203521699102$$
$$x_{5} = -75.9218224617533$$
$$x_{6} = 67.9930410026934$$
$$x_{7} = -31.9395253114962$$
$$x_{8} = 77.8666179139756$$
$$x_{9} = 60.2138591938044$$
$$x_{10} = -25.6563400043166$$
$$x_{11} = -34.0339204138894$$
$$x_{12} = 32.0891249616672$$
$$x_{13} = 14.1371670183814$$
$$x_{14} = 97.9129710368819$$
$$x_{15} = -29.8451301045666$$
$$x_{16} = 94.0233801324374$$
$$x_{17} = -3.81479107935903$$
$$x_{18} = -99.8577664891041$$
$$x_{19} = 17.7275585452567$$
$$x_{20} = 100.007366139275$$
$$x_{21} = 70.6858344638218$$
$$x_{22} = 95.8185760209241$$
$$x_{23} = 28.4987333575646$$
$$x_{24} = -54.0802735367957$$
$$x_{25} = -565.711077121419$$
$$x_{26} = -49.5922840316675$$
$$x_{27} = -19.0739553967952$$
$$x_{28} = 12.0427718387609$$
$$x_{29} = -37.9235113183339$$
$$x_{30} = -65.7490462501292$$
$$x_{31} = -47.7970882296161$$
$$x_{32} = -63.9538504480779$$
$$x_{33} = -59.1666616426078$$
$$x_{34} = 62.3082542961976$$
$$x_{35} = -2.01959527730772$$
$$x_{36} = -19.9715532978208$$
$$x_{37} = 18.3259571459405$$
$$x_{38} = -10.0979763865386$$
$$x_{39} = -83.7010042706423$$
$$x_{40} = -88.1889937757706$$
$$x_{41} = 92.2281843303861$$
$$x_{42} = -55.875469338847$$
$$x_{43} = 91.3305864293604$$
$$x_{44} = 48.245887180129$$
$$x_{45} = -80.1106125927377$$
$$x_{46} = 22.215548050385$$
$$x_{47} = 30.2939291596159$$
$$x_{48} = -93.5745811819246$$
$$x_{49} = 26.7035375043796$$
$$x_{50} = 41.9627018729494$$
$$x_{51} = 64.4026493237344$$
$$x_{52} = 50.0410829821803$$
$$x_{53} = -98.0625706870528$$
$$x_{54} = -97.1649727860272$$
$$x_{55} = -15.1843644923507$$
$$x_{56} = 72.4810305078217$$
$$x_{57} = -81.905808468591$$
$$x_{58} = -23.561944982403$$
$$x_{59} = 74.276226309873$$
$$x_{60} = 4.26359002987186$$
$$x_{61} = 7.85398171699378$$
$$x_{62} = -21.7667490998721$$
$$x_{63} = -69.6386371545737$$
$$x_{64} = -27.7507351067098$$
$$x_{65} = -134.864084629105$$
$$x_{66} = -39.7187071203852$$
$$x_{67} = -0.224399475256414$$
$$x_{68} = -44.2066966255135$$
$$x_{69} = -91.7793853798732$$
$$x_{70} = -78.0162175641465$$
$$x_{71} = -5.60998688141034$$
$$x_{72} = -89.9841895778219$$
$$x_{73} = 40.1675060708981$$
$$x_{74} = 21.3179501493593$$
$$x_{75} = 82.3546074191039$$
$$x_{76} = 76.0714221119243$$
$$x_{77} = -36.1283154371752$$
$$x_{78} = -46.0018924275648$$
$$x_{79} = -10.9955742670532$$
$$x_{80} = 85.9449990232065$$
$$x_{81} = 58.1194640115966$$
$$x_{82} = -170.768000670131$$
$$x_{83} = 56.025068989018$$
$$x_{84} = 24.0107438524363$$
$$x_{85} = -67.5442421328493$$
$$x_{86} = -73.8274272817975$$
$$x_{87} = -62.1586546460266$$
$$x_{88} = -57.6706651408984$$
$$x_{89} = 43.7578976750007$$
$$x_{90} = -13.6883679906412$$
$$x_{91} = 16.2315620435473$$
$$x_{92} = 84.1498032211552$$
$$x_{93} = 66.1978452006421$$
$$x_{94} = -11.8931721885899$$
$$x_{95} = 51.8362788697287$$
$$x_{96} = 6.05878583192317$$
$$x_{97} = 38.3723102688468$$
$$x_{98} = 9.94837673636768$$
$$x_{99} = 53.9306738866248$$