El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$4 \sin{\left(x \right)} + 5 \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \operatorname{atan}{\left(\frac{5}{4} \right)}$$
Solución numérica$$x_{1} = -16.6040186525203$$
$$x_{2} = 2.24553726901845$$
$$x_{3} = 83.9269462623531$$
$$x_{4} = -10.3208333453407$$
$$x_{5} = 90.2101315695327$$
$$x_{6} = -35.4535745740591$$
$$x_{7} = 5.38712992260824$$
$$x_{8} = -44.8783525348285$$
$$x_{9} = 14.8119078833776$$
$$x_{10} = 61.9357976872245$$
$$x_{11} = -26.0287966132897$$
$$x_{12} = 11.6703152297878$$
$$x_{13} = -7.17924069175093$$
$$x_{14} = -41.7367598812387$$
$$x_{15} = 99.634909530302$$
$$x_{16} = 80.7853536087633$$
$$x_{17} = 58.7942050336347$$
$$x_{18} = -73.1526864171366$$
$$x_{19} = 33.6614638049164$$
$$x_{20} = 149.900391987739$$
$$x_{21} = 17.9535005369674$$
$$x_{22} = -600.940252220222$$
$$x_{23} = 27.3782784977368$$
$$x_{24} = 68.2189829944041$$
$$x_{25} = -82.577464377906$$
$$x_{26} = 21.0950931905572$$
$$x_{27} = 46.2278344192756$$
$$x_{28} = -66.869501109957$$
$$x_{29} = 8.52872257619804$$
$$x_{30} = -29.1703892668795$$
$$x_{31} = -79.4358717243162$$
$$x_{32} = -57.4447231491876$$
$$x_{33} = -63.7279084563672$$
$$x_{34} = -51.161537842008$$
$$x_{35} = 65.0773903408143$$
$$x_{36} = -38.5951672276489$$
$$x_{37} = -85.7190570314958$$
$$x_{38} = -19.7456113061101$$
$$x_{39} = -88.8606496850855$$
$$x_{40} = 71.3605756479939$$
$$x_{41} = 30.5198711513266$$
$$x_{42} = -76.2942790707264$$
$$x_{43} = 77.6437609551735$$
$$x_{44} = -48.0199451884182$$
$$x_{45} = -95.1438349922651$$
$$x_{46} = -22.8872039596999$$
$$x_{47} = -0.896055384571344$$
$$x_{48} = 256.714542209792$$
$$x_{49} = 49.3694270728653$$
$$x_{50} = -54.3031304955978$$
$$x_{51} = -92.0022423386753$$
$$x_{52} = -32.3119819204693$$
$$x_{53} = 43.0862417656858$$
$$x_{54} = 93.3517242231225$$
$$x_{55} = -60.5863158027774$$
$$x_{56} = 52.5110197264551$$
$$x_{57} = -70.0110937635468$$
$$x_{58} = -4.03764803816114$$
$$x_{59} = 24.236685844147$$
$$x_{60} = 55.6526123800449$$
$$x_{61} = -13.4624259989305$$
$$x_{62} = 36.8030564585062$$
$$x_{63} = 39.944649112096$$
$$x_{64} = 87.0685389159429$$
$$x_{65} = 96.4933168767122$$
$$x_{66} = 74.5021683015837$$
$$x_{67} = -98.2854276458549$$