Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\frac{\cos{\left(\frac{x}{2} \right)}}{2} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \pi$$
$$x_{2} = 3 \pi$$
Numerical solution$$x_{1} = 40.8407044966673$$
$$x_{2} = 53.4070751110265$$
$$x_{3} = 97.3893722612836$$
$$x_{4} = 34.5575191894877$$
$$x_{5} = 47.1238898038469$$
$$x_{6} = -97.3893722612836$$
$$x_{7} = -21.9911485751286$$
$$x_{8} = 3.14159265358979$$
$$x_{9} = 65.9734457253857$$
$$x_{10} = -53.4070751110265$$
$$x_{11} = -9.42477796076938$$
$$x_{12} = -34.5575191894877$$
$$x_{13} = -9591.28237140964$$
$$x_{14} = 21.9911485751286$$
$$x_{15} = -47.1238898038469$$
$$x_{16} = 28.2743338823081$$
$$x_{17} = -3.14159265358979$$
$$x_{18} = -65.9734457253857$$
$$x_{19} = 72.2566310325652$$
$$x_{20} = -59.6902604182061$$
$$x_{21} = 7517042.68028432$$
$$x_{22} = -91.106186954104$$
$$x_{23} = 59.6902604182061$$
$$x_{24} = -40.8407044966673$$
$$x_{25} = 91.106186954104$$
$$x_{26} = 78.5398163397448$$
$$x_{27} = 84.8230016469244$$
$$x_{28} = 9.42477796076938$$
$$x_{29} = -160.221225333079$$
$$x_{30} = -84.8230016469244$$
$$x_{31} = -78.5398163397448$$
$$x_{32} = 15.707963267949$$
$$x_{33} = -28.2743338823081$$
$$x_{34} = -15.707963267949$$
$$x_{35} = -72.2566310325652$$