El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\tan{\left(x + \frac{\pi}{6} \right)} + 1 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{5 \pi}{12}$$
Solución numérica$$x_{1} = -60.9992573572018$$
$$x_{2} = 20.6821516361328$$
$$x_{3} = 74.0892267471593$$
$$x_{4} = -98.6983692002793$$
$$x_{5} = -4.45058959258554$$
$$x_{6} = 70.9476340935695$$
$$x_{7} = -42.1497014356631$$
$$x_{8} = 80.3724120543389$$
$$x_{9} = -51.5744793964324$$
$$x_{10} = -29.5833308213039$$
$$x_{11} = 33.248522250492$$
$$x_{12} = 52.0980781720307$$
$$x_{13} = -79.8488132787406$$
$$x_{14} = -82.9904059323304$$
$$x_{15} = 26.9653369433124$$
$$x_{16} = -67.2824426643814$$
$$x_{17} = -48.4328867428426$$
$$x_{18} = -39.0081087820733$$
$$x_{19} = 4.97418836818384$$
$$x_{20} = 42.6733002112614$$
$$x_{21} = -70.4240353179712$$
$$x_{22} = 55.2396708256205$$
$$x_{23} = -17.0169602069447$$
$$x_{24} = -86.1319985859202$$
$$x_{25} = 58.3812634792103$$
$$x_{26} = -32.7249234748937$$
$$x_{27} = -57.857664703612$$
$$x_{28} = 36.3901149040818$$
$$x_{29} = -76.7072206251508$$
$$x_{30} = 8.11578102177363$$
$$x_{31} = 14.3989663289532$$
$$x_{32} = 92.9387826686981$$
$$x_{33} = -7.59218224617533$$
$$x_{34} = 77.2308194007491$$
$$x_{35} = -73.565627971561$$
$$x_{36} = 83.5140047079287$$
$$x_{37} = -45.2912940892529$$
$$x_{38} = -89.27359123951$$
$$x_{39} = 86.6555973615185$$
$$x_{40} = 89.7971900151083$$
$$x_{41} = 30.1069295969022$$
$$x_{42} = -26.4417381677141$$
$$x_{43} = 48.9564855184409$$
$$x_{44} = -20.1585528605345$$
$$x_{45} = -64.1408500107916$$
$$x_{46} = 64.6644487863899$$
$$x_{47} = 96.0803753222878$$
$$x_{48} = -95.5567765466895$$
$$x_{49} = 45.8148928648512$$
$$x_{50} = -13.8753675533549$$
$$x_{51} = -35.8665161284835$$
$$x_{52} = -23.3001455141243$$
$$x_{53} = -54.7160720500222$$
$$x_{54} = -101.839961853869$$
$$x_{55} = 11.2573736753634$$
$$x_{56} = 17.540558982543$$
$$x_{57} = 61.5228561328001$$
$$x_{58} = -92.4151838930998$$
$$x_{59} = 39.5317075576716$$
$$x_{60} = 1.83259571459405$$
$$x_{61} = 23.8237442897226$$
$$x_{62} = 99.2219679758776$$
$$x_{63} = -10.7337748997651$$
$$x_{64} = 67.8060414399797$$
$$x_{65} = -1.30899693899575$$