Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\cos^{3}{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{\pi}{2}$$
$$x_{2} = \frac{3 \pi}{2}$$
Numerical solution$$x_{1} = -58.1194276545353$$
$$x_{2} = -80.1105785507599$$
$$x_{3} = 4.71229368085888$$
$$x_{4} = 70.6857435758276$$
$$x_{5} = -83.2523004207065$$
$$x_{6} = 48.6945935926021$$
$$x_{7} = 67.5443333859623$$
$$x_{8} = -92.6770895717702$$
$$x_{9} = -73.827410994311$$
$$x_{10} = -23.5619897288019$$
$$x_{11} = 1.57080273224359$$
$$x_{12} = -7.85396939058216$$
$$x_{13} = -83.2523059178598$$
$$x_{14} = -39.2700061565569$$
$$x_{15} = 73.8274768053124$$
$$x_{16} = 23.5620444336803$$
$$x_{17} = 14.1371748405436$$
$$x_{18} = -42.4114638604687$$
$$x_{19} = 26.7034598912501$$
$$x_{20} = 58.1194603256925$$
$$x_{21} = 42.4114617473496$$
$$x_{22} = 89.5354940921686$$
$$x_{23} = -29.8451152214988$$
$$x_{24} = -17.2788562472482$$
$$x_{25} = -67.5442906223714$$
$$x_{26} = 29.8451754771722$$
$$x_{27} = -61.2611560468397$$
$$x_{28} = 51.8363261592826$$
$$x_{29} = 67.5443442271897$$
$$x_{30} = 36.128317789764$$
$$x_{31} = -20.4202554438585$$
$$x_{32} = -45.5531401844306$$
$$x_{33} = -20.4203505482106$$
$$x_{34} = 20.4203112367381$$
$$x_{35} = 4.71228651848371$$
$$x_{36} = 80.1106035284868$$
$$x_{37} = 48.6946439323886$$
$$x_{38} = 26.7034436275456$$
$$x_{39} = -36.1282768063468$$
$$x_{40} = 86.3937628262857$$
$$x_{41} = 23.5619763533234$$
$$x_{42} = 92.6770059000324$$
$$x_{43} = -86.3937054164085$$
$$x_{44} = 70.6858302611407$$
$$x_{45} = -51.8362625267018$$
$$x_{46} = -89.5354410428862$$
$$x_{47} = -61.2611644481175$$
$$x_{48} = 7.85402475701276$$
$$x_{49} = -95.8185603030962$$
$$x_{50} = -64.4025554047934$$
$$x_{51} = 95.818627417042$$
$$x_{52} = -14.1371260033657$$
$$x_{53} = 45.553194340988$$
$$x_{54} = 1.5708945053691$$
$$x_{55} = 92.6768935770301$$
$$x_{56} = -1.57083925518957$$
$$x_{57} = -42.411405413931$$
$$x_{58} = 45.5531567451367$$
$$x_{59} = 64.4026122770508$$