Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\cos^{2}{\left(x \right)} = 0$$
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$$x_{1} = 89.5353908552844$$
$$x_{2} = -45.5530935883361$$
$$x_{3} = -32.9867231091652$$
$$x_{4} = 48.6946859238715$$
$$x_{5} = 83.2522055730903$$
$$x_{6} = 51.8362788999928$$
$$x_{7} = -39.2699083866483$$
$$x_{8} = 23.5619449395428$$
$$x_{9} = 61.2610569989704$$
$$x_{10} = -42.4115006098842$$
$$x_{11} = -17.2787590276524$$
$$x_{12} = 83.2522052340866$$
$$x_{13} = -32.9867227513827$$
$$x_{14} = -70.685834448838$$
$$x_{15} = 10.9955743696636$$
$$x_{16} = 10.9955740392793$$
$$x_{17} = 95.8185760590309$$
$$x_{18} = -58.1194639993376$$
$$x_{19} = -76.9690202568697$$
$$x_{20} = -23.5619450090417$$
$$x_{21} = -26.7035372990183$$
$$x_{22} = -51.8362786897497$$
$$x_{23} = -39.2699081528781$$
$$x_{24} = 26.7035373461441$$
$$x_{25} = 29.845130320338$$
$$x_{26} = 80.1106126771746$$
$$x_{27} = 32.9867226137576$$
$$x_{28} = 42.4115007291722$$
$$x_{29} = -1.57079642969308$$
$$x_{30} = -4.7123889912442$$
$$x_{31} = 39.2699081179815$$
$$x_{32} = -98.960168684456$$
$$x_{33} = -7.85398149857354$$
$$x_{34} = -83.2522055415057$$
$$x_{35} = -98.9601684414698$$
$$x_{36} = 86.393797888273$$
$$x_{37} = 70.6858345016621$$
$$x_{38} = -54.9778716831146$$
$$x_{39} = 73.8274274795554$$
$$x_{40} = -73.8274272800405$$
$$x_{41} = -89.5353907467661$$
$$x_{42} = -20.4203520321877$$
$$x_{43} = -92.6769830239371$$
$$x_{44} = 4.71238876848081$$
$$x_{45} = -80.1106125795659$$
$$x_{46} = 17.2787595624179$$
$$x_{47} = 76.9690200400775$$
$$x_{48} = -4.71238872430683$$
$$x_{49} = 36.1283156002139$$
$$x_{50} = -70.6858346386357$$
$$x_{51} = 32.986722928111$$
$$x_{52} = 80.1106131434937$$
$$x_{53} = -86.393797765473$$
$$x_{54} = -36.1283154192437$$
$$x_{55} = 39.2699084246933$$
$$x_{56} = -76.9690198771149$$
$$x_{57} = -95.8185758681287$$
$$x_{58} = 20.4203521497111$$
$$x_{59} = 67.5442422779275$$
$$x_{60} = 54.9778711883962$$
$$x_{61} = 58.1194644379895$$
$$x_{62} = 98.9601683381274$$
$$x_{63} = -26.7035375427973$$
$$x_{64} = 76.9690197631883$$
$$x_{65} = 23.5619451230057$$
$$x_{66} = -54.9778713137198$$
$$x_{67} = -14.1371668392726$$
$$x_{68} = -48.6946860920117$$
$$x_{69} = 54.9778714849733$$
$$x_{70} = 64.4026493086922$$
$$x_{71} = -61.2610569641117$$
$$x_{72} = -64.4026491876462$$
$$x_{73} = 92.6769830795146$$
$$x_{74} = -17.2787598091171$$
$$x_{75} = 541.924732890135$$
$$x_{76} = -10.9955745350309$$
$$x_{77} = -67.5442421675773$$
$$x_{78} = -48.6946858738636$$
$$x_{79} = 76.9690207492347$$
$$x_{80} = 45.553093700501$$
$$x_{81} = 7.85398174058521$$
$$x_{82} = 98.9601685932308$$
$$x_{83} = 61.2610566752601$$
$$x_{84} = 14.1371671048484$$
$$x_{85} = -61.2610562242523$$
$$x_{86} = -10.9955741902138$$
$$x_{87} = 17.2787598502655$$
$$x_{88} = 1.5707965454425$$
$$x_{89} = -98.96016883042$$
$$x_{90} = -29.8451300963672$$
$$x_{91} = -92.6769831823972$$