El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\frac{\sin{\left(8 x \right)}}{\tan^{2}{\left(5 x \right)} \cot{\left(3 x \right)}} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \frac{\pi}{8}$$
Solución numérica$$x_{1} = 4.0840704606004$$
$$x_{2} = -43.6681379206901$$
$$x_{3} = 81.9955682638974$$
$$x_{4} = 54.3495528530231$$
$$x_{5} = 79.5870138909414$$
$$x_{6} = -85.7654794540767$$
$$x_{7} = -83.7758040957278$$
$$x_{8} = -92.0486646786617$$
$$x_{9} = 90.1637091431017$$
$$x_{10} = -65.6592864924134$$
$$x_{11} = 26.0752190201569$$
$$x_{12} = 68.172560583868$$
$$x_{13} = -23.9546439836222$$
$$x_{14} = 70.0575161516737$$
$$x_{15} = 93.9336203825052$$
$$x_{16} = -93.9336204254789$$
$$x_{17} = 61.889375228658$$
$$x_{18} = 24.1902634542764$$
$$x_{19} = -16.0221225106729$$
$$x_{20} = 32.3584043293622$$
$$x_{21} = -26.075218919614$$
$$x_{22} = 5.96902607091754$$
$$x_{23} = 48.0663675835174$$
$$x_{24} = 98.3318499899683$$
$$x_{25} = -4.08407034014021$$
$$x_{26} = 2.19911488207896$$
$$x_{27} = 39.8982267758535$$
$$x_{28} = 76.3407014159574$$
$$x_{29} = 56.8628270273554$$
$$x_{30} = -51.8362786815231$$
$$x_{31} = -95.8185758680245$$
$$x_{32} = -97.703531526049$$
$$x_{33} = -48.0663675037548$$
$$x_{34} = -73.8274272777072$$
$$x_{35} = -55.7632696012188$$
$$x_{36} = 84.5088423324891$$
$$x_{37} = -70.0575160904909$$
$$x_{38} = -68.0678408277789$$
$$x_{39} = -1.96349540849362$$
$$x_{40} = 60.0044196781483$$
$$x_{41} = 78.2256570938239$$
$$x_{42} = 30.2378292908018$$
$$x_{43} = -19.7920336938887$$
$$x_{44} = 64.009950316892$$
$$x_{45} = -53.7212343925829$$
$$x_{46} = 10.3672558026092$$
$$x_{47} = -31.7300858140222$$
$$x_{48} = 16.0221225047861$$
$$x_{49} = -77.7544181763474$$
$$x_{50} = 20.0276531666349$$
$$x_{51} = -80.110612703956$$
$$x_{52} = 71.9424718067689$$
$$x_{53} = 74.2201264410589$$
$$x_{54} = -87.6504350605101$$
$$x_{55} = -46.1814119414824$$
$$x_{56} = 22.3053078070749$$
$$x_{57} = 38.0132710916724$$
$$x_{58} = -38.0132710937965$$
$$x_{59} = 56.2345085114092$$
$$x_{60} = -13.7444678594553$$
$$x_{61} = 12.2522113473755$$
$$x_{62} = 14.7654854459781$$
$$x_{63} = -81.9955682641137$$
$$x_{64} = -90.0589894029074$$
$$x_{65} = 49.9513232295974$$
$$x_{66} = 8.24668071567321$$
$$x_{67} = -61.7846555205993$$
$$x_{68} = 92.0486647239583$$
$$x_{69} = -60.0044196783785$$
$$x_{70} = 46.1814120216464$$
$$x_{71} = 44.2964563856823$$
$$x_{72} = -99.7455667514759$$
$$x_{73} = -33.7721210260903$$
$$x_{74} = 17.9070782300193$$
$$x_{75} = -49.9513232555573$$
$$x_{76} = 66.2876049652275$$
$$x_{77} = -39.8982266801284$$
$$x_{78} = 34.2433599291993$$
$$x_{79} = -9.73893723381938$$
$$x_{80} = -63.7743308534719$$
$$x_{81} = 86.0010988920206$$
$$x_{82} = 100.216805676295$$
$$x_{83} = -75.7123829677639$$
$$x_{84} = 42.0188017417635$$
$$x_{85} = 88.278753545553$$
$$x_{86} = -27.9601746691207$$
$$x_{87} = -5.96902608223638$$
$$x_{88} = -21.6769893464598$$
$$x_{89} = 52.2289778659303$$
$$x_{90} = -17.9070781008954$$
$$x_{91} = -59.3761011436045$$
$$x_{92} = 27.9601746509926$$
$$x_{93} = -71.9424718411691$$
$$x_{94} = -41.7831822726009$$