El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\cot{\left(12 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{\pi}{24}$$
Solución numérica$$x_{1} = 47.5165888855456$$
$$x_{2} = -91.4988860358027$$
$$x_{3} = -21.5984494934298$$
$$x_{4} = 75.0055246044563$$
$$x_{5} = -46.7311907221482$$
$$x_{6} = 24.2164433714213$$
$$x_{7} = -62.177354602298$$
$$x_{8} = -75.5291233800546$$
$$x_{9} = 63.7481509290929$$
$$x_{10} = -15.0534647984511$$
$$x_{11} = -51.4435797025329$$
$$x_{12} = 29.7142305152035$$
$$x_{13} = -99.8764664453755$$
$$x_{14} = -19.7658537788358$$
$$x_{15} = 100.400065220974$$
$$x_{16} = 22.1220482690281$$
$$x_{17} = -68.4605399094776$$
$$x_{18} = -29.9760299030026$$
$$x_{19} = -87.5718952188155$$
$$x_{20} = 81.2887099116359$$
$$x_{21} = 84.1685031774265$$
$$x_{22} = 86.2628982798197$$
$$x_{23} = -11.6500727570621$$
$$x_{24} = -40.7098048027677$$
$$x_{25} = -96.7348737917857$$
$$x_{26} = 89.9280897090078$$
$$x_{27} = 59.2975613365073$$
$$x_{28} = -57.4649656219133$$
$$x_{29} = -3.27249234748937$$
$$x_{30} = 14.2680666350536$$
$$x_{31} = 41.233403578366$$
$$x_{32} = -7.46128255227576$$
$$x_{33} = 80.2415123604393$$
$$x_{34} = -63.7481509290929$$
$$x_{35} = 3.27249234748937$$
$$x_{36} = -29.7142305152035$$
$$x_{37} = -2.22529479629277$$
$$x_{38} = 78.4089166458453$$
$$x_{39} = -0.916297857297023$$
$$x_{40} = -80.2415123604393$$
$$x_{41} = 9.55567765466895$$
$$x_{42} = 12.9590696960579$$
$$x_{43} = 15.5770635740494$$
$$x_{44} = 43.8513974563575$$
$$x_{45} = 92.022484811401$$
$$x_{46} = -34.4266194955881$$
$$x_{47} = 6.67588438887831$$
$$x_{48} = -18.7186562276392$$
$$x_{49} = -78.1471172580461$$
$$x_{50} = 62.9627527656954$$
$$x_{51} = -69.7695368484733$$
$$x_{52} = 42.2806011295626$$
$$x_{53} = 46.7311907221482$$
$$x_{54} = -13.7444678594553$$
$$x_{55} = -6.15228561328001$$
$$x_{56} = -37.3064127613788$$
$$x_{57} = 37.3064127613788$$
$$x_{58} = 19.5040543910366$$
$$x_{59} = -71.6021325630674$$
$$x_{60} = 76.8381203190504$$
$$x_{61} = -57.9885643975116$$
$$x_{62} = 52.4907772537295$$
$$x_{63} = 8.24668071567321$$
$$x_{64} = 25.2636409226179$$
$$x_{65} = -49.872783375738$$
$$x_{66} = -86.0010988920206$$
$$x_{67} = 30.4996286786009$$
$$x_{68} = -43.5895980685584$$
$$x_{69} = -41.7570023539643$$
$$x_{70} = -94.6404786893925$$
$$x_{71} = 93.8550805259951$$
$$x_{72} = -24.4782427592205$$
$$x_{73} = -90.7134878724053$$
$$x_{74} = -35.7356164345839$$
$$x_{75} = -9.03207887907065$$
$$x_{76} = -53.0143760293278$$
$$x_{77} = 68.9841386850759$$
$$x_{78} = 50.3963821513363$$
$$x_{79} = 87.5718952188155$$
$$x_{80} = -93.8550805259951$$
$$x_{81} = 56.941366846315$$
$$x_{82} = 34.4266194955881$$
$$x_{83} = 66.1043454192852$$
$$x_{84} = -27.8816348006094$$
$$x_{85} = -59.0357619487082$$
$$x_{86} = 58.2503637853107$$
$$x_{87} = -81.2887099116359$$
$$x_{88} = -64.009950316892$$
$$x_{89} = 53.2761754171269$$
$$x_{90} = 31.2850268419984$$
$$x_{91} = 97.7820713429823$$
$$x_{92} = 72.1257313386657$$
$$x_{93} = 36.2592152101822$$
$$x_{94} = -25.2636409226179$$