El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\frac{\sin{\left(2 x \right)}}{5} + \frac{3 \cos{\left(2 x \right)}}{5} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\operatorname{atan}{\left(3 \right)}}{2}$$
Solución numérica$$x_{1} = 13.5126440549549$$
$$x_{2} = -77.5935428991491$$
$$x_{3} = 76.3444971267508$$
$$x_{4} = 46.4993669176478$$
$$x_{5} = 55.9241448784172$$
$$x_{6} = -71.3103575919695$$
$$x_{7} = 82.6276824339304$$
$$x_{8} = -30.4696530953022$$
$$x_{9} = -332.062547839922$$
$$x_{10} = -11.6200971737634$$
$$x_{11} = -47.748412690046$$
$$x_{12} = -32.0404494220971$$
$$x_{13} = -1103.32354429622$$
$$x_{14} = 77.9152934535457$$
$$x_{15} = -24.1864677881226$$
$$x_{16} = -49.3192090168409$$
$$x_{17} = 57.4949412052121$$
$$x_{18} = -76.0227465723542$$
$$x_{19} = 62.2073301855967$$
$$x_{20} = -68.1687649383797$$
$$x_{21} = 48.0701632444427$$
$$x_{22} = 27.649810996109$$
$$x_{23} = -52.4608016704307$$
$$x_{24} = -90.1599135135082$$
$$x_{25} = 40.2161816104682$$
$$x_{26} = 93.6232567214947$$
$$x_{27} = -46.1776163632511$$
$$x_{28} = 90.4816640679049$$
$$x_{29} = 60.6365338588018$$
$$x_{30} = 35.5037926300835$$
$$x_{31} = 29.2206073229039$$
$$x_{32} = -91.7307098403031$$
$$x_{33} = 16.6542367085447$$
$$x_{34} = 10.3710514013651$$
$$x_{35} = -16.3324861541481$$
$$x_{36} = -8.47850452017361$$
$$x_{37} = -19.4740788077379$$
$$x_{38} = 2.51706976739067$$
$$x_{39} = 98.3356457018794$$
$$x_{40} = -69.7395612651746$$
$$x_{41} = -96.4430988206878$$
$$x_{42} = -54.0315979972256$$
$$x_{43} = 99.9064420286743$$
$$x_{44} = 5.65866242098046$$
$$x_{45} = -60.3147833044052$$
$$x_{46} = -61.8855796312001$$
$$x_{47} = -83.8767282063287$$
$$x_{48} = 70.0613118195712$$
$$x_{49} = 38.6453852836733$$
$$x_{50} = 68.4905154927763$$
$$x_{51} = 92.0524603946998$$
$$x_{52} = 96.7648493750845$$
$$x_{53} = -3.76611553978892$$
$$x_{54} = -39.8944310560715$$
$$x_{55} = 32.3621999764937$$
$$x_{56} = -17.903282480943$$
$$x_{57} = 33.9329963032886$$
$$x_{58} = 41.7869779372631$$
$$x_{59} = -33.611245748892$$
$$x_{60} = -5.33691186658382$$
$$x_{61} = -10.0493008469685$$
$$x_{62} = 79.4860897803406$$
$$x_{63} = -93.301506167098$$
$$x_{64} = -27.3280604417124$$
$$x_{65} = 85.7692750875202$$
$$x_{66} = 84.1984787607253$$
$$x_{67} = -82.3059318795337$$
$$x_{68} = -41.4652273828664$$
$$x_{69} = 26.0790146693141$$
$$x_{70} = -2.19531921299402$$
$$x_{71} = -25.7572641149175$$
$$x_{72} = -99.5846914742776$$
$$x_{73} = 11.94184772816$$
$$x_{74} = 71.6321081463661$$
$$x_{75} = -38.3236347292766$$
$$x_{76} = -98.0138951474827$$
$$x_{77} = 24.5082183425192$$
$$x_{78} = 19.7958293621345$$
$$x_{79} = 54.3533485516223$$
$$x_{80} = -308.500602937999$$
$$x_{81} = 18.2250330353396$$
$$x_{82} = -74.4519502455593$$
$$x_{83} = 63.7781265123916$$
$$x_{84} = 4.08786609418556$$
$$x_{85} = -55.6023943240205$$
$$x_{86} = -85.4475245331235$$
$$x_{87} = -63.456375957995$$
$$x_{88} = 49.6409595712376$$