Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sqrt{\cos{\left(x \right)} + 1} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \pi$$
Numerical solution$$x_{1} = 53.4070751110265$$
$$x_{2} = -97.3893722612836$$
$$x_{3} = 3.14159265358979$$
$$x_{4} = 97.3893722612836$$
$$x_{5} = 78.5398163397448$$
$$x_{6} = -84.8230016469244$$
$$x_{7} = -59.6902604182061$$
$$x_{8} = -65.9734457253857$$
$$x_{9} = 47.1238898038469$$
$$x_{10} = 21.9911485751286$$
$$x_{11} = -21.9911485751286$$
$$x_{12} = -15.707963267949$$
$$x_{13} = -34.5575191894877$$
$$x_{14} = 97.3893722612836$$
$$x_{15} = 34.5575191894877$$
$$x_{16} = 9.42477796076938$$
$$x_{17} = -40.8407044966673$$
$$x_{18} = 65.9734457253857$$
$$x_{19} = -3.1415926535898$$
$$x_{20} = -28.2743338823081$$
$$x_{21} = -53.4070751110265$$
$$x_{22} = -9.42477796076938$$
$$x_{23} = 40.8407044966673$$
$$x_{24} = -91.106186954104$$
$$x_{25} = 15.707963267949$$
$$x_{26} = 59.6902604182061$$
$$x_{27} = 21.9911485751286$$
$$x_{28} = 47.1238898038469$$
$$x_{29} = 91.106186954104$$
$$x_{30} = 28.2743338823081$$
$$x_{31} = -47.1238898038469$$
$$x_{32} = -3.14159265358979$$
$$x_{33} = -28.2743338823081$$
$$x_{34} = -72.2566310325652$$
$$x_{35} = -84.8230016469244$$
$$x_{36} = 84.8230016469244$$
$$x_{37} = 72.2566310325652$$
$$x_{38} = -78.5398163397448$$
$$x_{39} = 15.707963267949$$
$$x_{40} = 3.14159265358979$$