Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$3 \sin{\left(x \right)} - 4 \cos{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \operatorname{atan}{\left(\frac{4}{3} \right)}$$
Numerical solution$$x_{1} = -87.0372990825126$$
$$x_{2} = 92.0334821721056$$
$$x_{3} = -2.21429743558818$$
$$x_{4} = -21.0638533571269$$
$$x_{5} = -80.754113775333$$
$$x_{6} = 104.599852786465$$
$$x_{7} = -58357.297837866$$
$$x_{8} = -96.462077043282$$
$$x_{9} = -68.1877431609738$$
$$x_{10} = -30.4886313178963$$
$$x_{11} = -14.7806680499474$$
$$x_{12} = 41.7679997146689$$
$$x_{13} = -71.3293358145636$$
$$x_{14} = -39.9134092786657$$
$$x_{15} = 38.6264070610791$$
$$x_{16} = 66.9007409433873$$
$$x_{17} = -24.2054460107167$$
$$x_{18} = 95.1750748256954$$
$$x_{19} = -27.3470386643065$$
$$x_{20} = -5.35589008917797$$
$$x_{21} = -77.6125211217432$$
$$x_{22} = -33.6302239714861$$
$$x_{23} = -17.9222607035371$$
$$x_{24} = 35.4848144074893$$
$$x_{25} = 48.0511850218485$$
$$x_{26} = 13.4936658323608$$
$$x_{27} = -58.7629652002045$$
$$x_{28} = 10.352073178771$$
$$x_{29} = 60.6175556362077$$
$$x_{30} = -99.6036696968718$$
$$x_{31} = 70.0423335969771$$
$$x_{32} = 76.3255189041567$$
$$x_{33} = 22.9184437931302$$
$$x_{34} = 16.6352584859506$$
$$x_{35} = 19.7768511395404$$
$$x_{36} = -74.4709284681534$$
$$x_{37} = 57.4759629826179$$
$$x_{38} = -206.417819918925$$
$$x_{39} = -36.7718166250759$$
$$x_{40} = 44.9095923682587$$
$$x_{41} = 7.2104805251812$$
$$x_{42} = 29.2016291003098$$
$$x_{43} = 88.8918895185158$$
$$x_{44} = -49.3381872394351$$
$$x_{45} = -93.3204843896922$$
$$x_{46} = -65.046150507384$$
$$x_{47} = -11.6390753963576$$
$$x_{48} = -43.0550019322555$$
$$x_{49} = -52.4797798930249$$
$$x_{50} = 32.3432217538995$$
$$x_{51} = 63.7591482897975$$
$$x_{52} = 54.3343703290281$$
$$x_{53} = 82.6087042113362$$
$$x_{54} = -83.8957064289228$$
$$x_{55} = 98.3166674792852$$
$$x_{56} = 51.1927776754383$$
$$x_{57} = -8.49748274276777$$
$$x_{58} = 0.927295218001612$$
$$x_{59} = 73.1839262505669$$
$$x_{60} = 4.06888787159141$$
$$x_{61} = 85.750296864926$$
$$x_{62} = -90.1788917361024$$
$$x_{63} = -61.9045578537943$$
$$x_{64} = 26.06003644672$$
$$x_{65} = 79.4671115577464$$
$$x_{66} = -46.1965945858453$$
$$x_{67} = -55.6213725466147$$