Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(3 x \right)} - \cos{\left(2 x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{\pi}{10}$$
$$x_{2} = \frac{\pi}{2}$$
$$x_{3} = - i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
$$x_{4} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
$$x_{5} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
Numerical solution$$x_{1} = 21.6769893097696$$
$$x_{2} = -76.340701482232$$
$$x_{3} = -63.7743308678728$$
$$x_{4} = -3.45575191894877$$
$$x_{5} = 24.1902634326414$$
$$x_{6} = -70.0575161750524$$
$$x_{7} = 51.836278889862$$
$$x_{8} = 45.5530935642345$$
$$x_{9} = -36.1283154253128$$
$$x_{10} = -49.9513231920777$$
$$x_{11} = -57.4911455606932$$
$$x_{12} = 68.1725605828985$$
$$x_{13} = 763.092855556961$$
$$x_{14} = -9.73893722612836$$
$$x_{15} = 78.2256570743859$$
$$x_{16} = 6.59734457253857$$
$$x_{17} = 27.9601746169492$$
$$x_{18} = -98.960168969851$$
$$x_{19} = -42.4115008665293$$
$$x_{20} = 14.1371670842217$$
$$x_{21} = 84.5088423815654$$
$$x_{22} = 70.6858346085267$$
$$x_{23} = 94.5619388730528$$
$$x_{24} = -3082.21655243695$$
$$x_{25} = -100.216805649514$$
$$x_{26} = 58.1194641300388$$
$$x_{27} = -46.18141200777$$
$$x_{28} = -90.1637091580271$$
$$x_{29} = -5.96902604182061$$
$$x_{30} = -77.5973385436679$$
$$x_{31} = 48.0663675999238$$
$$x_{32} = 95.8185759411754$$
$$x_{33} = -60.0044196835651$$
$$x_{34} = -17.2787596488556$$
$$x_{35} = 4.08407044966673$$
$$x_{36} = 98.3318500573605$$
$$x_{37} = 30.473448739821$$
$$x_{38} = 44.2964564156161$$
$$x_{39} = 26.7035374759771$$
$$x_{40} = 7.85398173263687$$
$$x_{41} = -29.8451300991422$$
$$x_{42} = 61.8893752757189$$
$$x_{43} = 64.4026493135056$$
$$x_{44} = 11.6238928182822$$
$$x_{45} = -42.41150070898$$
$$x_{46} = 88.2787535658732$$
$$x_{47} = -12.2522113490002$$
$$x_{48} = 20.4203521560512$$
$$x_{49} = -19.7920337176157$$
$$x_{50} = 1.57079642986981$$
$$x_{51} = -87.6504350351552$$
$$x_{52} = -61.2610567621223$$
$$x_{53} = -39.8982267005904$$
$$x_{54} = 97.0752129959246$$
$$x_{55} = -2.19911485751286$$
$$x_{56} = 95.8185760463912$$
$$x_{57} = -93.9336203423348$$
$$x_{58} = 340.862803294903$$
$$x_{59} = 85.7654794430014$$
$$x_{60} = 54.3495529071034$$
$$x_{61} = -16.0221225333079$$
$$x_{62} = 92.0486647501809$$
$$x_{63} = 71.9424717672063$$
$$x_{64} = 50.5796417227957$$
$$x_{65} = 20.4203523376058$$
$$x_{66} = -53.7212343763855$$
$$x_{67} = -86.3937978510561$$
$$x_{68} = 34.2433599241287$$
$$x_{69} = -43.6681378848981$$
$$x_{70} = -56.2345084992573$$
$$x_{71} = -80.1106125840384$$
$$x_{72} = -23.5619448484475$$
$$x_{73} = 0.314159265358979$$
$$x_{74} = -22.3053078404875$$
$$x_{75} = -37.3849525777185$$
$$x_{76} = 38.0132711084365$$
$$x_{77} = -66.2876049907446$$
$$x_{78} = -83.8805238508475$$
$$x_{79} = 74.4557458900781$$
$$x_{80} = -97.7035315266426$$
$$x_{81} = 10.3672557568463$$
$$x_{82} = -67.5442421572865$$
$$x_{83} = -36.1283156488921$$
$$x_{84} = 41.7831822927443$$
$$x_{85} = -23.5619450008864$$
$$x_{86} = 83.2522057062651$$
$$x_{87} = 81.9955682586936$$
$$x_{88} = -26.0752190247953$$
$$x_{89} = 17.9070781254618$$
$$x_{90} = -81.3672497279756$$
$$x_{91} = 65.6592864600267$$
$$x_{92} = -73.8274272806455$$
$$x_{93} = 89.5353906921091$$
$$x_{94} = -13.5088484104361$$
$$x_{95} = -33.6150413934108$$