El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$3 \cos{\left(\frac{x - \pi}{4} \right)} + 1 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \pi - 4 \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = 4 \operatorname{asin}{\left(\frac{1}{3} \right)} + 3 \pi$$
Solución numérica$$x_{1} = 86.1823492847409$$
$$x_{2} = -89.7468393162875$$
$$x_{3} = -29.6336815201246$$
$$x_{4} = 61.0496080560226$$
$$x_{5} = -54.766422748843$$
$$x_{6} = -79.8991639775613$$
$$x_{7} = 45.7645421660304$$
$$x_{8} = -4.50094029140628$$
$$x_{9} = -140.012321773724$$
$$x_{10} = 161.580572970896$$
$$x_{11} = -64.6140980875692$$
$$x_{12} = 20.6318009373121$$
$$x_{13} = 96.0300246234671$$
$$x_{14} = 136.447831742178$$
$$x_{15} = -155.297387663716$$
$$x_{16} = -39.4813568588508$$
$$x_{17} = -4980.78370357764$$
$$x_{18} = 70.8972833947488$$
$$x_{19} = -114.879580545006$$
$$x_{20} = -105.03190520628$$
$$x_{21} = 9269.48057310566$$
$$x_{22} = 10.7841255985859$$
$$x_{23} = -190.277804231161$$
$$x_{24} = 35.9168668273042$$
$$x_{25} = -14.3486156301325$$