El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(4 \sin{\left(2 x \right)} + 3 \cos{\left(2 x \right)}\right) - 3 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 0$$
$$x_{2} = \operatorname{atan}{\left(\frac{4}{3} \right)}$$
Solución numérica$$x_{1} = 48.0511850218485$$
$$x_{2} = -15.707963267949$$
$$x_{3} = 13.4936658323608$$
$$x_{4} = -31.4159265358979$$
$$x_{5} = 84.8230016469244$$
$$x_{6} = 21.9911485751286$$
$$x_{7} = 0$$
$$x_{8} = -21.9911485751286$$
$$x_{9} = -96.462077043282$$
$$x_{10} = 28.2743338823081$$
$$x_{11} = -24.2054460107167$$
$$x_{12} = -30.4886313178963$$
$$x_{13} = 70.0423335969771$$
$$x_{14} = 72.2566310325652$$
$$x_{15} = -99.6036696968718$$
$$x_{16} = -1086.99105814207$$
$$x_{17} = -94.2477796076938$$
$$x_{18} = 54.3343703290281$$
$$x_{19} = -25.1327412287183$$
$$x_{20} = 87.9645943005142$$
$$x_{21} = -50.2654824574367$$
$$x_{22} = -43.9822971502571$$
$$x_{23} = -97.3893722612836$$
$$x_{24} = 50.2654824574367$$
$$x_{25} = -74.4709284681534$$
$$x_{26} = 26.06003644672$$
$$x_{27} = -83.8957064289228$$
$$x_{28} = 76.3255189041567$$
$$x_{29} = -91.106186954104$$
$$x_{30} = 106.814150222053$$
$$x_{31} = 98.3166674792852$$
$$x_{32} = -53.4070751110265$$
$$x_{33} = 12.5663706143592$$
$$x_{34} = -81.6814089933346$$
$$x_{35} = 94.2477796076938$$
$$x_{36} = 92.0334821721056$$
$$x_{37} = 85.750296864926$$
$$x_{38} = 79.4671115577464$$
$$x_{39} = 32.3432217538995$$
$$x_{40} = -8.49748274276777$$
$$x_{41} = -68.1877431609738$$
$$x_{42} = -11.6390753963576$$
$$x_{43} = -28.2743338823081$$
$$x_{44} = -17.9222607035371$$
$$x_{45} = -72.2566310325652$$
$$x_{46} = 29.2016291003098$$
$$x_{47} = 65.9734457253857$$
$$x_{48} = 35.4848144074893$$
$$x_{49} = 19.7768511395404$$
$$x_{50} = -87.9645943005142$$
$$x_{51} = 40.8407044966673$$
$$x_{52} = 62.8318530717959$$
$$x_{53} = 47.1238898038469$$
$$x_{54} = 57.4759629826179$$
$$x_{55} = 78.5398163397448$$
$$x_{56} = -6.28318530717959$$
$$x_{57} = 15.707963267949$$
$$x_{58} = 63.7591482897975$$
$$x_{59} = -77.6125211217432$$
$$x_{60} = -3.14159265358979$$
$$x_{61} = 56.5486677646163$$
$$x_{62} = -2.21429743558818$$
$$x_{63} = -90.1788917361024$$
$$x_{64} = -69.1150383789755$$
$$x_{65} = -65.9734457253857$$
$$x_{66} = 43.9822971502571$$
$$x_{67} = -55.6213725466147$$
$$x_{68} = -37.6991118430775$$
$$x_{69} = -59.6902604182061$$
$$x_{70} = -61.9045578537943$$
$$x_{71} = 10.352073178771$$
$$x_{72} = -33.6302239714861$$
$$x_{73} = -75.398223686155$$
$$x_{74} = 100.530964914873$$
$$x_{75} = 82.6087042113362$$
$$x_{76} = 34.5575191894877$$
$$x_{77} = 6.28318530717959$$
$$x_{78} = -47.1238898038469$$
$$x_{79} = 18.8495559215388$$
$$x_{80} = 41.7679997146689$$
$$x_{81} = -9.42477796076938$$
$$x_{82} = 4.06888787159141$$
$$x_{83} = -39.9134092786657$$
$$x_{84} = -46.1965945858453$$
$$x_{85} = -52.4797798930249$$