El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\cos^{2}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{35}\right) - \frac{1}{35} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \operatorname{acos}{\left(- \frac{1}{5} \right)} + 2 \pi$$
$$x_{2} = - \operatorname{acos}{\left(\frac{1}{7} \right)} + 2 \pi$$
$$x_{3} = \operatorname{acos}{\left(- \frac{1}{5} \right)}$$
$$x_{4} = \operatorname{acos}{\left(\frac{1}{7} \right)}$$
Solución numérica$$x_{1} = -20.2770046794283$$
$$x_{2} = 52.0376367050219$$
$$x_{3} = 20.2770046794283$$
$$x_{4} = -1.77215424758523$$
$$x_{5} = -86.192440052929$$
$$x_{6} = 17.0774016739535$$
$$x_{7} = 92.4756253601086$$
$$x_{8} = 290.453972888151$$
$$x_{9} = -73.9707749282655$$
$$x_{10} = -98.7588106672882$$
$$x_{11} = 76.8256724440446$$
$$x_{12} = -32.8433752937875$$
$$x_{13} = -7.71063406506912$$
$$x_{14} = -11.1389218564696$$
$$x_{15} = -48.4933282098515$$
$$x_{16} = 36.271663085188$$
$$x_{17} = 83.1088577512241$$
$$x_{18} = 23.7052924708288$$
$$x_{19} = 73.9707749282655$$
$$x_{20} = -155.307478431904$$
$$x_{21} = -10.7942163667739$$
$$x_{22} = 70.542487136865$$
$$x_{23} = 98.7588106672882$$
$$x_{24} = 45.7544513978423$$
$$x_{25} = -54.776513517031$$
$$x_{26} = 26.5601899866079$$
$$x_{27} = 61.0596988242106$$
$$x_{28} = -92.4756253601086$$
$$x_{29} = -83.4535632409198$$
$$x_{30} = 39.1265606009671$$
$$x_{31} = -64.2593018296854$$
$$x_{32} = 8.05533955476481$$
$$x_{33} = 99.1035161569839$$
$$x_{34} = -45.7544513978423$$
$$x_{35} = 438.050817254986$$
$$x_{36} = 13.9938193722487$$
$$x_{37} = -79.9092547457494$$
$$x_{38} = 2263.37415934254$$
$$x_{39} = 10.7942163667739$$
$$x_{40} = -48.8380336995472$$
$$x_{41} = -70.542487136865$$
$$x_{42} = -23.7052924708288$$
$$x_{43} = 29.9884777780084$$
$$x_{44} = -33.1880807834832$$
$$x_{45} = 54.776513517031$$
$$x_{46} = -35.9269575954923$$
$$x_{47} = -29.9884777780084$$
$$x_{48} = -13.9938193722487$$
$$x_{49} = -26.5601899866079$$
$$x_{50} = 1.77215424758523$$
$$x_{51} = 48.8380336995472$$
$$x_{52} = 77.1703779337403$$
$$x_{53} = -96.019933855279$$
$$x_{54} = 92.8203308498043$$
$$x_{55} = 55.1212190067267$$
$$x_{56} = 4.51103105959436$$
$$x_{57} = 11.1389218564696$$
$$x_{58} = -70.8871926265607$$
$$x_{59} = -76.8256724440446$$
$$x_{60} = -77.1703779337403$$
$$x_{61} = -4383.89119016377$$
$$x_{62} = -61.4044043139063$$
$$x_{63} = -51.6929312153262$$
$$x_{64} = -99.1035161569839$$
$$x_{65} = -4.51103105959436$$
$$x_{66} = -42.2101429026719$$
$$x_{67} = 64.2593018296854$$
$$x_{68} = -26.9048954763036$$
$$x_{69} = 17.4221071636492$$
$$x_{70} = 48.4933282098515$$
$$x_{71} = -4.85573654929006$$
$$x_{72} = -89.7367485480994$$
$$x_{73} = 89.7367485480994$$
$$x_{74} = -61.0596988242106$$
$$x_{75} = -55.1212190067267$$
$$x_{76} = 83.4535632409198$$
$$x_{77} = 32.8433752937875$$
$$x_{78} = 57.9761165225058$$
$$x_{79} = 39.4712660906627$$
$$x_{80} = 42.2101429026719$$
$$x_{81} = -39.4712660906627$$
$$x_{82} = 86.192440052929$$
$$x_{83} = 67.6875896210859$$
$$x_{84} = -17.4221071636492$$
$$x_{85} = 61.4044043139063$$
$$x_{86} = 80.2539602354451$$
$$x_{87} = -67.6875896210859$$
$$x_{88} = 33.1880807834832$$
$$x_{89} = 96.019933855279$$
$$x_{90} = -57.9761165225058$$