El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$5 \sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \operatorname{atan}{\left(\frac{2}{5} \right)}$$
Solución numérica$$x_{1} = 12.1858642372468$$
$$x_{2} = -160.601731710192$$
$$x_{3} = 9.04427158365701$$
$$x_{4} = 56.1681613875039$$
$$x_{5} = 53.0265687339141$$
$$x_{6} = 84.4424952698121$$
$$x_{7} = 2.76108627647743$$
$$x_{8} = 71.8761246554529$$
$$x_{9} = 59.3097540410937$$
$$x_{10} = 15.3274568908366$$
$$x_{11} = -0.380506377112365$$
$$x_{12} = -85.2035080240368$$
$$x_{13} = -9.80528433788174$$
$$x_{14} = -97.769878638396$$
$$x_{15} = 93.8672732305814$$
$$x_{16} = -94.6282859848062$$
$$x_{17} = 75.0177173090427$$
$$x_{18} = -100.911471291986$$
$$x_{19} = 46.7433834267345$$
$$x_{20} = 78.1593099626325$$
$$x_{21} = -3.52209903070216$$
$$x_{22} = -6.66369168429195$$
$$x_{23} = -91.4866933312164$$
$$x_{24} = -47.5043961809593$$
$$x_{25} = 62.4513466946835$$
$$x_{26} = 5.90267893006722$$
$$x_{27} = -31.7964329130103$$
$$x_{28} = 100.150458537761$$
$$x_{29} = -34.9380255666001$$
$$x_{30} = -25.5132476058307$$
$$x_{31} = 31.0354201587856$$
$$x_{32} = -88.3451006776266$$
$$x_{33} = -63.2123594489082$$
$$x_{34} = -82.061915370447$$
$$x_{35} = 87.5840879234018$$
$$x_{36} = -12.9468769914715$$
$$x_{37} = -19.2300622986511$$
$$x_{38} = -44.3628035273695$$
$$x_{39} = 24.752234851606$$
$$x_{40} = -69.4955447560878$$
$$x_{41} = -50.6459888345491$$
$$x_{42} = -28.6548402594205$$
$$x_{43} = 90.7256805769916$$
$$x_{44} = -66.353952102498$$
$$x_{45} = -75.7787300632674$$
$$x_{46} = 40.4601981195549$$
$$x_{47} = 34.1770128123754$$
$$x_{48} = 97.0088658841712$$
$$x_{49} = -78.9203227168572$$
$$x_{50} = -53.7875814881388$$
$$x_{51} = -72.6371374096776$$
$$x_{52} = 18.4690495444264$$
$$x_{53} = -56.9291741417286$$
$$x_{54} = -22.3716549522409$$
$$x_{55} = -38.0796182201899$$
$$x_{56} = -60.0707667953184$$
$$x_{57} = -16.0884696450613$$
$$x_{58} = 43.6017907731447$$
$$x_{59} = 21.6106421980162$$
$$x_{60} = -41.2212108737797$$
$$x_{61} = 27.8938275051958$$
$$x_{62} = 37.3186054659652$$
$$x_{63} = 65.5929393482733$$
$$x_{64} = 49.8849760803243$$
$$x_{65} = 81.3009026162223$$
$$x_{66} = 68.7345320018631$$