El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left(\sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \sin{\left(3 x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = 0$$
$$x_{2} = - \frac{2 \pi}{3}$$
$$x_{3} = - \frac{\pi}{2}$$
$$x_{4} = \frac{\pi}{2}$$
$$x_{5} = \frac{2 \pi}{3}$$
$$x_{6} = \pi$$
Solución numérica$$x_{1} = -39.7935069454707$$
$$x_{2} = 73.8274273593601$$
$$x_{3} = 48.1710873550435$$
$$x_{4} = 70.6858347057703$$
$$x_{5} = -64.4026493985908$$
$$x_{6} = 14.1371669411541$$
$$x_{7} = -41.8879020478639$$
$$x_{8} = 90.0589894029074$$
$$x_{9} = 4.18879020478639$$
$$x_{10} = 14.6607657167524$$
$$x_{11} = -53.4070751110265$$
$$x_{12} = -67.5442420521806$$
$$x_{13} = 52.3598775598299$$
$$x_{14} = -114.668131856027$$
$$x_{15} = -20.4203522483337$$
$$x_{16} = 28.2743338823081$$
$$x_{17} = 50.2654824574367$$
$$x_{18} = 36.1283155162826$$
$$x_{19} = -2.0943951023932$$
$$x_{20} = -90.0589894029074$$
$$x_{21} = -33.5103216382911$$
$$x_{22} = 34.5575191894877$$
$$x_{23} = -29.845130209103$$
$$x_{24} = 65.9734457253857$$
$$x_{25} = 0$$
$$x_{26} = 23.5619449019235$$
$$x_{27} = 20.4203522483337$$
$$x_{28} = 78.5398163397448$$
$$x_{29} = 98.4365698124802$$
$$x_{30} = 59.6902604182061$$
$$x_{31} = 100.530964914873$$
$$x_{32} = -85.870199198121$$
$$x_{33} = -72.2566310325652$$
$$x_{34} = 21.9911485751286$$
$$x_{35} = -17.2787595947439$$
$$x_{36} = 84.8230016469244$$
$$x_{37} = -79.5870138909414$$
$$x_{38} = 79.5870138909414$$
$$x_{39} = -37.6991118430775$$
$$x_{40} = -81.6814089933346$$
$$x_{41} = -21.9911485751286$$
$$x_{42} = 26.7035375555132$$
$$x_{43} = -46.0766922526503$$
$$x_{44} = -58.1194640914112$$
$$x_{45} = -4.18879020478639$$
$$x_{46} = 64.4026493985908$$
$$x_{47} = 12.5663706143592$$
$$x_{48} = -87.9645943005142$$
$$x_{49} = -3.14159265358979$$
$$x_{50} = -77.4926187885482$$
$$x_{51} = 41.8879020478639$$
$$x_{52} = -14.1371669411541$$
$$x_{53} = -94.2477796076938$$
$$x_{54} = -51.8362787842316$$
$$x_{55} = 15.707963267949$$
$$x_{56} = -43.9822971502571$$
$$x_{57} = 39.7935069454707$$
$$x_{58} = -6.28318530717959$$
$$x_{59} = 58.1194640914112$$
$$x_{60} = -83.7758040957278$$
$$x_{61} = -28.2743338823081$$
$$x_{62} = -34.5575191894877$$
$$x_{63} = -95.8185759344887$$
$$x_{64} = 81.6814089933346$$
$$x_{65} = -75.398223686155$$
$$x_{66} = 94.2477796076938$$
$$x_{67} = -48.1710873550435$$
$$x_{68} = 46.0766922526503$$
$$x_{69} = -59.6902604182061$$
$$x_{70} = 87.9645943005142$$
$$x_{71} = -92.1533845053006$$
$$x_{72} = 2.0943951023932$$
$$x_{73} = -15.707963267949$$
$$x_{74} = -23.5619449019235$$
$$x_{75} = 83.7758040957278$$
$$x_{76} = -61.261056745001$$
$$x_{77} = -7.85398163397448$$
$$x_{78} = 67.5442420521806$$
$$x_{79} = 80.1106126665397$$
$$x_{80} = 96.342174710087$$
$$x_{81} = 6.28318530717959$$
$$x_{82} = 29.845130209103$$
$$x_{83} = -50.2654824574367$$
$$x_{84} = 54.4542726622231$$
$$x_{85} = -73.8274273593601$$
$$x_{86} = 37.6991118430775$$
$$x_{87} = -86.3937979737193$$
$$x_{88} = 43.9822971502571$$
$$x_{89} = 56.5486677646163$$
$$x_{90} = -65.9734457253857$$
$$x_{91} = 58.6430628670095$$
$$x_{92} = 92.1533845053006$$
$$x_{93} = -31.4159265358979$$
$$x_{94} = 35.6047167406843$$
$$x_{95} = 72.2566310325652$$
$$x_{96} = 10.471975511966$$