Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(6 x \right)} + 2 \cos{\left(3 x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = - \frac{5 \pi}{6}$$
$$x_{2} = - \frac{\pi}{2}$$
$$x_{3} = - \frac{\pi}{6}$$
$$x_{4} = \frac{\pi}{6}$$
$$x_{5} = \frac{\pi}{2}$$
$$x_{6} = \frac{5 \pi}{6}$$
Numerical solution$$x_{1} = -17.2787658184495$$
$$x_{2} = -27.7507349140879$$
$$x_{3} = -61.2610284419178$$
$$x_{4} = 89.5354065077626$$
$$x_{5} = 78.0162175641465$$
$$x_{6} = 72.7802507340821$$
$$x_{7} = -34.0339089404682$$
$$x_{8} = -12.0427718387609$$
$$x_{9} = 53.9306960771948$$
$$x_{10} = 64.4026139003315$$
$$x_{11} = 26.7035092327958$$
$$x_{12} = 82.2050077689329$$
$$x_{13} = -53.9306738866248$$
$$x_{14} = -97.9129710368819$$
$$x_{15} = 45.5531274936893$$
$$x_{16} = -95.8185759344887$$
$$x_{17} = 29.845130209103$$
$$x_{18} = 80.1106126665397$$
$$x_{19} = 36.1283155162826$$
$$x_{20} = -75.9218398742025$$
$$x_{21} = 84.2994028713261$$
$$x_{22} = -69.6386642264464$$
$$x_{23} = -7.85398163397448$$
$$x_{24} = -56.025068989018$$
$$x_{25} = -73.8274112345701$$
$$x_{26} = -63.3554344014648$$
$$x_{27} = -16.2315620435473$$
$$x_{28} = 38.2227106186758$$
$$x_{29} = 31.9395253114962$$
$$x_{30} = 56.0250605081548$$
$$x_{31} = 40.317105721069$$
$$x_{32} = 30.8923257529709$$
$$x_{33} = 97.9129980286252$$
$$x_{34} = -78.0162119738293$$
$$x_{35} = 9.94839375467499$$
$$x_{36} = -47.6474885794452$$
$$x_{37} = -25.6563631682447$$
$$x_{38} = -9.94837673636768$$
$$x_{39} = -91.6297857297023$$
$$x_{40} = -3.66519142918809$$
$$x_{41} = 75.9218224617533$$
$$x_{42} = 86.3937979737193$$
$$x_{43} = -5.75958653158129$$
$$x_{44} = 34.0339204138894$$
$$x_{45} = -29.8451155401915$$
$$x_{46} = 58.1194604293512$$
$$x_{47} = -100.007366139275$$
$$x_{48} = 16.2315668495577$$
$$x_{49} = 18.3259380577434$$
$$x_{50} = -80.1105798289775$$
$$x_{51} = 100.007363587005$$
$$x_{52} = -49.7418836818384$$
$$x_{53} = 60.2138684289819$$
$$x_{54} = 12.0427582893912$$
$$x_{55} = -31.9395421257451$$
$$x_{56} = -58.1194640914112$$
$$x_{57} = -51.8362787842316$$
$$x_{58} = -14.1371669411541$$
$$x_{59} = -88.4882197448468$$
$$x_{60} = -0.52356731973288$$
$$x_{61} = 62.3082394437526$$
$$x_{62} = -93.7241808320955$$
$$x_{63} = 42.4115008234622$$
$$x_{64} = 14.1371746311081$$
$$x_{65} = -71.7330366891137$$