El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x \sin{\left(x \right)} + \cos{\left(x \right)}} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución numérica$$x_{1} = -64.4181717218392$$
$$x_{2} = -45.57503179559$$
$$x_{3} = 70.69997803861$$
$$x_{4} = -51.855560729152$$
$$x_{5} = -48.7152107175577$$
$$x_{6} = -7.97866571241324$$
$$x_{7} = 89.5465575382492$$
$$x_{8} = -42.4350618814099$$
$$x_{9} = 64.4181717218392$$
$$x_{10} = 36.1559664195367$$
$$x_{11} = -29.8785865061074$$
$$x_{12} = -98.9702722883957$$
$$x_{13} = 45.57503179559$$
$$x_{14} = -73.8409691490209$$
$$x_{15} = 98.9702722883957$$
$$x_{16} = 95.8290108090195$$
$$x_{17} = 14.2074367251912$$
$$x_{18} = 80.1230928148503$$
$$x_{19} = -20.469167402741$$
$$x_{20} = 73.8409691490209$$
$$x_{21} = -58.1366632448992$$
$$x_{22} = 4.91318043943488$$
$$x_{23} = -17.3363779239834$$
$$x_{24} = -61.2773745335697$$
$$x_{25} = 23.6042847729804$$
$$x_{26} = -39.295350981473$$
$$x_{27} = 58.1366632448992$$
$$x_{28} = -54.9960525574964$$
$$x_{29} = 83.2642147040886$$
$$x_{30} = 39.295350981473$$
$$x_{31} = 20.469167402741$$
$$x_{32} = 51.855560729152$$
$$x_{33} = 92.687771772017$$
$$x_{34} = 17.3363779239834$$
$$x_{35} = 0$$
$$x_{36} = -67.5590428388084$$
$$x_{37} = -11.085538406497$$
$$x_{38} = 7.97866571241324$$
$$x_{39} = -95.8290108090195$$
$$x_{40} = -14.2074367251912$$
$$x_{41} = 67.5590428388084$$
$$x_{42} = -70.69997803861$$
$$x_{43} = -23.6042847729804$$
$$x_{44} = 11.085538406497$$
$$x_{45} = -4.91318043943488$$
$$x_{46} = -76.9820093304187$$
$$x_{47} = 2.02875783811043$$
$$x_{48} = -26.7409160147873$$
$$x_{49} = 26.7409160147873$$
$$x_{50} = 54.9960525574964$$
$$x_{51} = -89.5465575382492$$
$$x_{52} = -36.1559664195367$$
$$x_{53} = -83.2642147040886$$
$$x_{54} = 86.4053708116885$$
$$x_{55} = 61.2773745335697$$
$$x_{56} = 76.9820093304187$$
$$x_{57} = -92.687771772017$$
$$x_{58} = 42.4350618814099$$
$$x_{59} = -86.4053708116885$$
$$x_{60} = 48.7152107175577$$
$$x_{61} = -33.0170010333572$$
$$x_{62} = 33.0170010333572$$
$$x_{63} = -80.1230928148503$$
$$x_{64} = -2.02875783811043$$
$$x_{65} = 29.8785865061074$$