Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\frac{\cos{\left(x \right)}}{\frac{3}{2}} - \frac{3}{10} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = - \operatorname{acos}{\left(\frac{9}{20} \right)} + 2 \pi$$
$$x_{2} = \operatorname{acos}{\left(\frac{9}{20} \right)}$$
Numerical solution$$x_{1} = -42.8782661625095$$
$$x_{2} = -51.3695134451843$$
$$x_{3} = -13.6704016021068$$
$$x_{4} = -5.17915431943199$$
$$x_{5} = 57.6526987523639$$
$$x_{6} = 51.3695134451843$$
$$x_{7} = -76.5022546739026$$
$$x_{8} = -80.577378005587$$
$$x_{9} = 32.5199575236455$$
$$x_{10} = 5.17915431943199$$
$$x_{11} = -86.8605633127666$$
$$x_{12} = 89.0686252882618$$
$$x_{13} = 38.8031428308251$$
$$x_{14} = 74.2941926984074$$
$$x_{15} = 82.7854399810822$$
$$x_{16} = 26.2367722164659$$
$$x_{17} = -61.7278220840483$$
$$x_{18} = 11.4623396266116$$
$$x_{19} = -30.3118955481503$$
$$x_{20} = -17.7455249337912$$
$$x_{21} = -38.8031428308251$$
$$x_{22} = 1.1040309877476$$
$$x_{23} = -7.38721629492719$$
$$x_{24} = 45.0863281380047$$
$$x_{25} = 24.0287102409707$$
$$x_{26} = -36.5950808553299$$
$$x_{27} = 76.5022546739026$$
$$x_{28} = -32.5199575236455$$
$$x_{29} = -49.1614514696891$$
$$x_{30} = 42.8782661625095$$
$$x_{31} = -93.1437486199462$$
$$x_{32} = 7.38721629492719$$
$$x_{33} = 80.577378005587$$
$$x_{34} = -70.219069366723$$
$$x_{35} = -63.9358840595435$$
$$x_{36} = -11.4623396266116$$
$$x_{37} = -99.4269339271258$$
$$x_{38} = 55.4446367768687$$
$$x_{39} = -74.2941926984074$$
$$x_{40} = 36.5950808553299$$
$$x_{41} = 19.9535869092864$$
$$x_{42} = -68.0110073912278$$
$$x_{43} = 63.9358840595435$$
$$x_{44} = -19.9535869092864$$
$$x_{45} = 145.617293052878$$
$$x_{46} = -57.6526987523639$$
$$x_{47} = 95.3518105954414$$
$$x_{48} = 99.4269339271258$$
$$x_{49} = -89.0686252882618$$
$$x_{50} = -1.1040309877476$$
$$x_{51} = -55.4446367768687$$
$$x_{52} = -95.3518105954414$$
$$x_{53} = 70.219069366723$$
$$x_{54} = 49.1614514696891$$
$$x_{55} = -45.0863281380047$$
$$x_{56} = 30.3118955481503$$
$$x_{57} = -26.2367722164659$$
$$x_{58} = -24.0287102409707$$
$$x_{59} = 13.6704016021068$$
$$x_{60} = 68.0110073912278$$
$$x_{61} = 17.7455249337912$$
$$x_{62} = 61.7278220840483$$
$$x_{63} = 93.1437486199462$$
$$x_{64} = 86.8605633127666$$
$$x_{65} = -82.7854399810822$$