Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\cos^{4}{\left(x \right)} = 0$$
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$$x_{1} = -23.5624641310095$$
$$x_{2} = 89.5358464044975$$
$$x_{3} = 64.4022227094897$$
$$x_{4} = -67.5448065308884$$
$$x_{5} = 4.71186425026897$$
$$x_{6} = 80.1114831041243$$
$$x_{7} = -45.5536354157268$$
$$x_{8} = 95.8191611950437$$
$$x_{9} = 86.393394845477$$
$$x_{10} = 51.8368135303721$$
$$x_{11} = 20.4198789484825$$
$$x_{12} = -14.1367106446029$$
$$x_{13} = -58.1190619806665$$
$$x_{14} = 14.1376276021486$$
$$x_{15} = -39.2699360040648$$
$$x_{16} = 67.5449867319022$$
$$x_{17} = -80.110238235034$$
$$x_{18} = -1.57129267637417$$
$$x_{19} = 29.8456391715984$$
$$x_{20} = 29.8446819952113$$
$$x_{21} = 36.1288337410562$$
$$x_{22} = -7.85359055632515$$
$$x_{23} = -29.8448005950739$$
$$x_{24} = -83.2518382112953$$
$$x_{25} = -61.2608756650826$$
$$x_{26} = 42.4110507437587$$
$$x_{27} = 7.85446444955012$$
$$x_{28} = 26.7027138657113$$
$$x_{29} = -17.279021473451$$
$$x_{30} = -89.5359774768786$$
$$x_{31} = 58.1200312868449$$
$$x_{32} = -36.1278861189969$$
$$x_{33} = -51.8359986082336$$
$$x_{34} = -95.8183696553645$$
$$x_{35} = -73.8271872272585$$
$$x_{36} = 73.8279875350762$$