El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$3 \sin{\left(\frac{\pi x}{4} \right)} + 4 \cos{\left(\frac{\pi x}{4} \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{4 \operatorname{atan}{\left(\frac{4}{3} \right)}}{\pi}$$
Solución numérica$$x_{1} = -29.1806689412035$$
$$x_{2} = -57.1806689412035$$
$$x_{3} = 86.8193310587965$$
$$x_{4} = -81.1806689412035$$
$$x_{5} = 14.8193310587965$$
$$x_{6} = 58.8193310587965$$
$$x_{7} = 26.8193310587965$$
$$x_{8} = 46.8193310587965$$
$$x_{9} = 30.8193310587965$$
$$x_{10} = 62.8193310587965$$
$$x_{11} = -61.1806689412035$$
$$x_{12} = 2.81933105879653$$
$$x_{13} = 98.8193310587965$$
$$x_{14} = -49.1806689412035$$
$$x_{15} = 94.8193310587965$$
$$x_{16} = -101.180668941203$$
$$x_{17} = -77.1806689412035$$
$$x_{18} = 10.8193310587965$$
$$x_{19} = -45.1806689412035$$
$$x_{20} = 50.8193310587965$$
$$x_{21} = -69.1806689412035$$
$$x_{22} = -89.1806689412035$$
$$x_{23} = 82.8193310587965$$
$$x_{24} = 78.8193310587965$$
$$x_{25} = 54.8193310587965$$
$$x_{26} = -13.1806689412035$$
$$x_{27} = 90.8193310587965$$
$$x_{28} = 18.8193310587965$$
$$x_{29} = -53.1806689412035$$
$$x_{30} = -41.1806689412035$$
$$x_{31} = -93.1806689412035$$
$$x_{32} = -25.1806689412035$$
$$x_{33} = -65.1806689412035$$
$$x_{34} = -73.1806689412035$$
$$x_{35} = 22.8193310587965$$
$$x_{36} = -33.1806689412035$$
$$x_{37} = 74.8193310587965$$
$$x_{38} = 66.8193310587965$$
$$x_{39} = 34.8193310587965$$
$$x_{40} = -37.1806689412035$$
$$x_{41} = -21.1806689412035$$
$$x_{42} = 38.8193310587965$$
$$x_{43} = -9.18066894120347$$
$$x_{44} = 6.81933105879653$$
$$x_{45} = 42.8193310587965$$
$$x_{46} = -97.1806689412035$$
$$x_{47} = -5.18066894120347$$
$$x_{48} = 70.8193310587965$$
$$x_{49} = -17.1806689412035$$
$$x_{50} = -85.1806689412035$$
$$x_{51} = -1.18066894120347$$