El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\cos^{2}{\left(x \right)} - 6 \cos{\left(x \right)}\right) + 1 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \operatorname{acos}{\left(3 - 2 \sqrt{2} \right)} + 2 \pi$$
$$x_{2} = \operatorname{acos}{\left(3 - 2 \sqrt{2} \right)}$$
Solución numérica$$x_{1} = 57.9470380936983$$
$$x_{2} = 61.4334827427138$$
$$x_{3} = -32.81429686498$$
$$x_{4} = -1264.31861707218$$
$$x_{5} = -55.1502974355342$$
$$x_{6} = 4.88481497809754$$
$$x_{7} = -83.0797793224167$$
$$x_{8} = -23.7343708996363$$
$$x_{9} = -99.1325945857913$$
$$x_{10} = -42.5839268211751$$
$$x_{11} = 39.0974821721596$$
$$x_{12} = -80.2830386642526$$
$$x_{13} = -48.8671121283546$$
$$x_{14} = -177.32755893011$$
$$x_{15} = -11.1680002852771$$
$$x_{16} = 26.5311115578004$$
$$x_{17} = 23.7343708996363$$
$$x_{18} = -7.68155563626163$$
$$x_{19} = 55.1502974355342$$
$$x_{20} = 95.6461499367758$$
$$x_{21} = -1.39837032908205$$
$$x_{22} = 45.3806674793392$$
$$x_{23} = -39.0974821721596$$
$$x_{24} = -89.3629646295963$$
$$x_{25} = 5854.53033596229$$
$$x_{26} = -13.9647409434412$$
$$x_{27} = 92.8494092786117$$
$$x_{28} = 64.2302234008779$$
$$x_{29} = 80.2830386642526$$
$$x_{30} = -73.999853357073$$
$$x_{31} = -76.7965940152371$$
$$x_{32} = 20.2479262506208$$
$$x_{33} = 70.5134087080575$$
$$x_{34} = 83.0797793224167$$
$$x_{35} = -61.4334827427138$$
$$x_{36} = 13.9647409434412$$
$$x_{37} = 1.39837032908205$$
$$x_{38} = 7.68155563626163$$
$$x_{39} = -20.2479262506208$$
$$x_{40} = 89.3629646295963$$
$$x_{41} = -30.0175562068159$$
$$x_{42} = -70.5134087080575$$
$$x_{43} = 11.1680002852771$$
$$x_{44} = 30.0175562068159$$
$$x_{45} = 42.5839268211751$$
$$x_{46} = 73.999853357073$$
$$x_{47} = -17.4511855924567$$
$$x_{48} = -92.8494092786117$$
$$x_{49} = 48.8671121283546$$
$$x_{50} = 32.81429686498$$
$$x_{51} = -95.6461499367758$$
$$x_{52} = 67.7166680498934$$
$$x_{53} = -419.57504525195$$
$$x_{54} = -36.3007415139955$$
$$x_{55} = -64.2302234008779$$
$$x_{56} = -26.5311115578004$$
$$x_{57} = -57.9470380936983$$
$$x_{58} = -67.7166680498934$$
$$x_{59} = 86.5662239714322$$
$$x_{60} = 99.1325945857913$$
$$x_{61} = 36.3007415139955$$
$$x_{62} = 17.4511855924567$$
$$x_{63} = -4.88481497809754$$
$$x_{64} = 76.7965940152371$$
$$x_{65} = -86.5662239714322$$
$$x_{66} = -45.3806674793392$$
$$x_{67} = -51.6638527865187$$
$$x_{68} = 51.6638527865187$$