El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$2 \cos{\left(\frac{x}{2} \right)} + 1 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{4 \pi}{3}$$
$$x_{2} = \frac{8 \pi}{3}$$
Solución numérica$$x_{1} = -192.684349420174$$
$$x_{2} = 20.943951023932$$
$$x_{3} = -83.7758040957278$$
$$x_{4} = -92.1533845053006$$
$$x_{5} = 79.5870138909414$$
$$x_{6} = -79.5870138909414$$
$$x_{7} = -54.4542726622231$$
$$x_{8} = 16.7551608191456$$
$$x_{9} = -58.6430628670095$$
$$x_{10} = -29.3215314335047$$
$$x_{11} = 92.1533845053006$$
$$x_{12} = 4.18879020478639$$
$$x_{13} = 29.3215314335047$$
$$x_{14} = 33.5103216382911$$
$$x_{15} = -96.342174710087$$
$$x_{16} = -67.0206432765823$$
$$x_{17} = 54.4542726622231$$
$$x_{18} = 67.0206432765823$$
$$x_{19} = 58.6430628670095$$
$$x_{20} = -16.7551608191456$$
$$x_{21} = 46.0766922526503$$
$$x_{22} = -33.5103216382911$$
$$x_{23} = -4.18879020478639$$
$$x_{24} = -117.286125734019$$
$$x_{25} = -46.0766922526503$$
$$x_{26} = 8.37758040957278$$
$$x_{27} = 83.7758040957278$$
$$x_{28} = 96.342174710087$$
$$x_{29} = -20.943951023932$$
$$x_{30} = 71.2094334813686$$
$$x_{31} = 41.8879020478639$$
$$x_{32} = -8.37758040957278$$
$$x_{33} = -71.2094334813686$$
$$x_{34} = -41.8879020478639$$