El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(2 \cos^{2}{\left(x \right)} + \cos{\left(x \right)}\right) - 1 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{\pi}{3}$$
$$x_{2} = \pi$$
$$x_{3} = \frac{5 \pi}{3}$$
Solución numérica$$x_{1} = 82.7286065445312$$
$$x_{2} = -97.3893724356252$$
$$x_{3} = 9.42477818680547$$
$$x_{4} = -26.1799387799149$$
$$x_{5} = -5.23598775598299$$
$$x_{6} = 65.9734457528689$$
$$x_{7} = 32.4631240870945$$
$$x_{8} = -39867.8579716057$$
$$x_{9} = -78.5398161151012$$
$$x_{10} = -53.4070752795041$$
$$x_{11} = -93.2005820564972$$
$$x_{12} = -40.8407044128941$$
$$x_{13} = 40.8407042778045$$
$$x_{14} = 28.2743338652086$$
$$x_{15} = 26.1799387799149$$
$$x_{16} = -28.2743337200245$$
$$x_{17} = -9.42477812311019$$
$$x_{18} = 19.8967534727354$$
$$x_{19} = 91.1061868116125$$
$$x_{20} = 91.1061868861836$$
$$x_{21} = -47.1238905036874$$
$$x_{22} = 47.1238898268985$$
$$x_{23} = -7.33038285837618$$
$$x_{24} = 24.0855436775217$$
$$x_{25} = -11.5191730631626$$
$$x_{26} = 91.1061869261407$$
$$x_{27} = 68.0678408277789$$
$$x_{28} = 55.5014702134197$$
$$x_{29} = 99.4837673636768$$
$$x_{30} = 36.6519142918809$$
$$x_{31} = 21.9911485973609$$
$$x_{32} = -76.4454212373516$$
$$x_{33} = -24.0855436775217$$
$$x_{34} = -30.3687289847013$$
$$x_{35} = -68.0678408277789$$
$$x_{36} = -70.162235930172$$
$$x_{37} = 61.7846555205993$$
$$x_{38} = 17.8023583703422$$
$$x_{39} = 34.5575190335478$$
$$x_{40} = 80.634211442138$$
$$x_{41} = 38.7463093942741$$
$$x_{42} = 47.1238894268221$$
$$x_{43} = -13.6135681655558$$
$$x_{44} = -32.4631240870945$$
$$x_{45} = -99.4837673636768$$
$$x_{46} = -84.8230014829768$$
$$x_{47} = 57.5958653158129$$
$$x_{48} = -40.8407047547408$$
$$x_{49} = -34.5575189638817$$
$$x_{50} = 59.6902605931502$$
$$x_{51} = 84.8230014287926$$
$$x_{52} = -59.690260457585$$
$$x_{53} = 30.3687289847013$$
$$x_{54} = 3.14159276530697$$
$$x_{55} = -95.2949771588904$$
$$x_{56} = 97.389372486408$$
$$x_{57} = 47.1238897752019$$
$$x_{58} = -17.8023583703422$$
$$x_{59} = 107.86134777325$$
$$x_{60} = -3.14159287255706$$
$$x_{61} = 15.7079634367135$$
$$x_{62} = -65.9734457650482$$
$$x_{63} = -91.1061871711313$$
$$x_{64} = -47.1238900222279$$
$$x_{65} = 11.5191730631626$$
$$x_{66} = -40.8407049942712$$
$$x_{67} = -63.8790506229925$$
$$x_{68} = -61.7846555205993$$
$$x_{69} = 63.8790506229925$$
$$x_{70} = 74.3510261349584$$
$$x_{71} = 91.1061863890352$$
$$x_{72} = 78.5398161904624$$
$$x_{73} = -719.424718069224$$
$$x_{74} = -21.9911485864549$$
$$x_{75} = 3.14159271706432$$
$$x_{76} = 47.1238901206303$$
$$x_{77} = 53.4070753369186$$
$$x_{78} = 3.14159322994749$$
$$x_{79} = -84.8230015251551$$
$$x_{80} = -74.3510261349584$$
$$x_{81} = -51.3126800086333$$
$$x_{82} = -72.256630877064$$
$$x_{83} = 13.6135681655558$$
$$x_{84} = -57.5958653158129$$
$$x_{85} = -19.8967534727354$$
$$x_{86} = 72.2566310277195$$
$$x_{87} = -40.8407044009017$$
$$x_{88} = -55.5014702134197$$
$$x_{89} = -84.8230022421807$$
$$x_{90} = -646.120889088301$$
$$x_{91} = 76.4454212373516$$
$$x_{92} = -15.7079632965016$$
$$x_{93} = -49.2182849062401$$
$$x_{94} = 21.9911485851931$$
$$x_{95} = 3.14159267447126$$
$$x_{96} = 70.162235930172$$