El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$5 \sin{\left(x \right)} - 3 \cos{\left(x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = \operatorname{atan}{\left(\frac{3}{5} \right)}$$
Solución numérica$$x_{1} = -65.4330262251151$$
$$x_{2} = -87.4241748002436$$
$$x_{3} = -81.140989493064$$
$$x_{4} = 57.0890872648869$$
$$x_{5} = 47.6643093041175$$
$$x_{6} = 97.9297917615542$$
$$x_{7} = 9.96519746103996$$
$$x_{8} = 69.655457879246$$
$$x_{9} = -46.5834703035763$$
$$x_{10} = -40.3002849963967$$
$$x_{11} = 85.363421147195$$
$$x_{12} = -77.9993968394742$$
$$x_{13} = -5.742765806909$$
$$x_{14} = 75.9386431864256$$
$$x_{15} = -18.3091364212682$$
$$x_{16} = 35.0979386897583$$
$$x_{17} = 94.7881991079644$$
$$x_{18} = 946.159808230798$$
$$x_{19} = -96.848952761013$$
$$x_{20} = -49.7250629571661$$
$$x_{21} = -34.0170996892171$$
$$x_{22} = -93.7073601074232$$
$$x_{23} = 66.5138652256562$$
$$x_{24} = -30.8755070356273$$
$$x_{25} = -21.450729074858$$
$$x_{26} = 25.6731607289889$$
$$x_{27} = 13.1067901146298$$
$$x_{28} = 63.3722725720664$$
$$x_{29} = 0.540419500270584$$
$$x_{30} = 79.0802358400154$$
$$x_{31} = 6.82360480745017$$
$$x_{32} = -24.5923217284478$$
$$x_{33} = 53.9474946112971$$
$$x_{34} = -12.0259511140886$$
$$x_{35} = 16.2483827682195$$
$$x_{36} = 346.115611395148$$
$$x_{37} = 38.2395313433481$$
$$x_{38} = -59.1498409179355$$
$$x_{39} = 60.2306799184767$$
$$x_{40} = -90.5657674538334$$
$$x_{41} = -2.60117315331921$$
$$x_{42} = 91.6466064543746$$
$$x_{43} = -68.5746188787049$$
$$x_{44} = 19.3899754218093$$
$$x_{45} = -84.2825821466538$$
$$x_{46} = -71.7162115322947$$
$$x_{47} = 3.68201215386038$$
$$x_{48} = -43.4418776499865$$
$$x_{49} = 31.9563460361685$$
$$x_{50} = -52.8666556107559$$
$$x_{51} = -8.8843584604988$$
$$x_{52} = 72.7970505328358$$
$$x_{53} = 50.8059019577073$$
$$x_{54} = -56.0082482643457$$
$$x_{55} = 41.3811239969379$$
$$x_{56} = -62.2914335715253$$
$$x_{57} = 28.8147533825787$$
$$x_{58} = 22.5315680753991$$
$$x_{59} = -27.7339143820376$$
$$x_{60} = -74.8578041858844$$
$$x_{61} = 82.2218284936052$$
$$x_{62} = 44.5227166505277$$
$$x_{63} = -99.9905454146028$$
$$x_{64} = 101.071384415144$$
$$x_{65} = -15.1675437676784$$
$$x_{66} = -37.1586923428069$$
$$x_{67} = 88.5050138007848$$
$$x_{68} = -125.123286643321$$