El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$- \sin{\left(3 x \right)} + \cos{\left(6 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{5 \pi}{6}$$
$$x_{2} = - \frac{\pi}{6}$$
$$x_{3} = \frac{\pi}{18}$$
$$x_{4} = \frac{\pi}{2}$$
$$x_{5} = \frac{17 \pi}{18}$$
Solución numérica$$x_{1} = -29.8451301109422$$
$$x_{2} = 0.174532925199433$$
$$x_{3} = 66.4970446696463$$
$$x_{4} = 2.26892802759263$$
$$x_{5} = -89.884456477708$$
$$x_{6} = 23.9110107523223$$
$$x_{7} = -67.5442420688214$$
$$x_{8} = 100.007366129847$$
$$x_{9} = -91.9788515801012$$
$$x_{10} = -54.9778717037312$$
$$x_{11} = -94.0732466824944$$
$$x_{12} = -61.9591884457987$$
$$x_{13} = -6.10865238198015$$
$$x_{14} = -80.1106126031829$$
$$x_{15} = 34.3829862642883$$
$$x_{16} = 42.0624349730633$$
$$x_{17} = -20.0712863979348$$
$$x_{18} = -99.6583002888762$$
$$x_{19} = 12.0427717580055$$
$$x_{20} = -82.2050077507738$$
$$x_{21} = -87.7900613753148$$
$$x_{22} = -45.9021593274509$$
$$x_{23} = -69.6386372104483$$
$$x_{24} = -13.7881010907552$$
$$x_{25} = 31.5904594610974$$
$$x_{26} = 26.0054058547155$$
$$x_{27} = -73.8274272830703$$
$$x_{28} = -46.6002911740461$$
$$x_{29} = 51.8362788424787$$
$$x_{30} = 39.9680398706701$$
$$x_{31} = -84.9975345721239$$
$$x_{32} = 7.85398169704974$$
$$x_{33} = -31.9395254595335$$
$$x_{34} = 9.94837677950866$$
$$x_{35} = 48.3456202802429$$
$$x_{36} = 92.3279174305$$
$$x_{37} = -11.693705988362$$
$$x_{38} = 57.4213323906134$$
$$x_{39} = 76.2708883121522$$
$$x_{40} = 32.2885911618951$$
$$x_{41} = 64.4026493396976$$
$$x_{42} = -34.0339203821021$$
$$x_{43} = -55.6760031386191$$
$$x_{44} = 88.1391272257137$$
$$x_{45} = -59.8647933434055$$
$$x_{46} = -71.7330322689197$$
$$x_{47} = 83.9503370209273$$
$$x_{48} = -25.6563400551229$$
$$x_{49} = 16.2315620580819$$
$$x_{50} = 44.1568300754565$$
$$x_{51} = -38.2227106541004$$
$$x_{52} = 62.308254260218$$
$$x_{53} = -1.91986217719376$$
$$x_{54} = 5.75958638151864$$
$$x_{55} = -36.8264472170804$$
$$x_{56} = -41.7133691226645$$
$$x_{57} = 60.2138592240795$$
$$x_{58} = -17.9768912955416$$
$$x_{59} = -85.6956662729216$$
$$x_{60} = 53.930673938486$$
$$x_{61} = -36.1283154517589$$
$$x_{62} = 81.8559419185341$$
$$x_{63} = 86.0447321233204$$
$$x_{64} = 90.2335223281068$$
$$x_{65} = -50.0909495322373$$
$$x_{66} = 49.0437519810407$$
$$x_{67} = -43.8077642250577$$
$$x_{68} = -64.0535835481919$$
$$x_{69} = 78.3652834145454$$
$$x_{70} = -27.7507351061625$$
$$x_{71} = 56.0250689508787$$
$$x_{72} = 72.0820981073658$$
$$x_{73} = 18.3259571018334$$
$$x_{74} = 74.176493209759$$
$$x_{75} = 46.2512251778497$$
$$x_{76} = -96.8657734510647$$
$$x_{77} = 28.0998009571087$$
$$x_{78} = -23.5619449440496$$
$$x_{79} = 20.4203521942729$$
$$x_{80} = -47.9965544298441$$
$$x_{81} = -15.8824961931484$$
$$x_{82} = -57.7703982410123$$
$$x_{83} = -9.59931088596881$$
$$x_{84} = -52.8834763542084$$
$$x_{85} = 97.9129710951409$$
$$x_{86} = -78.0162175469573$$
$$x_{87} = 69.9877030049726$$
$$x_{88} = 37.873644768277$$
$$x_{89} = 95.818575982716$$
$$x_{90} = 30.1941960595019$$
$$x_{91} = -4.01425727958696$$