El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$2 \sin{\left(3 x + \frac{\pi}{4} \right)} - 1 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\pi}{36}$$
$$x_{2} = \frac{7 \pi}{36}$$
Solución numérica$$x_{1} = -37.7863783056772$$
$$x_{2} = 82.2922742315326$$
$$x_{3} = -29.4087978961045$$
$$x_{4} = 8.29031394697306$$
$$x_{5} = 54.3670061996234$$
$$x_{6} = -79.6742803535411$$
$$x_{7} = 29.9323966717028$$
$$x_{8} = -64.315382935991$$
$$x_{9} = -2.18166156499291$$
$$x_{10} = 25.7436064669164$$
$$x_{11} = -73.3910950463616$$
$$x_{12} = -55.9378025264183$$
$$x_{13} = -48.2583538176432$$
$$x_{14} = -35.691983203284$$
$$x_{15} = -90.1462558655071$$
$$x_{16} = 78.1034840267462$$
$$x_{17} = -95.731309471889$$
$$x_{18} = 73.9146938219599$$
$$x_{19} = -18.2386906833407$$
$$x_{20} = 14.5734992541527$$
$$x_{21} = 84.3866693339258$$
$$x_{22} = -51.7490123216319$$
$$x_{23} = -491.571983824203$$
$$x_{24} = 23.6492113645232$$
$$x_{25} = 34.1211868764891$$
$$x_{26} = 80.1978791291394$$
$$x_{27} = -5.67232006898157$$
$$x_{28} = 87.8773278379145$$
$$x_{29} = -0.0872664625997165$$
$$x_{30} = -3.57792496658838$$
$$x_{31} = 43.8950306876574$$
$$x_{32} = -41.9751685104636$$
$$x_{33} = -53.8434074240251$$
$$x_{34} = 96.2549082474873$$
$$x_{35} = -88.0518607631139$$
$$x_{36} = -26.6162710929135$$
$$x_{37} = 67.6315085147803$$
$$x_{38} = 64.8389817115893$$
$$x_{39} = 58.5557964044098$$
$$x_{40} = -81.7686754559343$$
$$x_{41} = -9.86111027376796$$
$$x_{42} = 4.10152374218667$$
$$x_{43} = 38.3099770812755$$
$$x_{44} = 83.6885376331281$$
$$x_{45} = -85.9574656607207$$
$$x_{46} = 2.00712863979348$$
$$x_{47} = -39.8807734080704$$
$$x_{48} = 98.3493033498805$$
$$x_{49} = 52.2726110972302$$
$$x_{50} = -77.579885251148$$
$$x_{51} = 48.0838208924438$$
$$x_{52} = 12.4791041517595$$
$$x_{53} = 45.9894257900506$$
$$x_{54} = -11.9555053761612$$
$$x_{55} = 40.4043721836687$$
$$x_{56} = 10.3847090493663$$
$$x_{57} = -99.9200996766754$$
$$x_{58} = -49.6546172192387$$
$$x_{59} = 56.4614013020166$$
$$x_{60} = 27.8380015693096$$
$$x_{61} = 69.7259036171735$$
$$x_{62} = -16.1442955809475$$
$$x_{63} = -62.2209878335978$$
$$x_{64} = -58.0321976288115$$
$$x_{65} = 15.2716309549504$$
$$x_{66} = 100.443698452274$$
$$x_{67} = 36.2155819788823$$
$$x_{68} = 76.0090889243531$$
$$x_{69} = 1072.24302596272$$
$$x_{70} = 60.650191506803$$
$$x_{71} = -66.4097780383842$$
$$x_{72} = -33.5975881008908$$
$$x_{73} = -70.5985682431706$$
$$x_{74} = 71.8202987195667$$
$$x_{75} = 89.9717229403077$$
$$x_{76} = -23.1256125889249$$
$$x_{77} = 50.178215994837$$
$$x_{78} = -20.3330857857339$$
$$x_{79} = -31.5031929984976$$
$$x_{80} = 6.19591884457987$$
$$x_{81} = 32.0267917740959$$
$$x_{82} = -46.16395871525$$
$$x_{83} = -83.8630705583275$$
$$x_{84} = -7.76671517137477$$
$$x_{85} = -14.0499004785544$$
$$x_{86} = 92.0661180427009$$
$$x_{87} = 20.8566845613322$$
$$x_{88} = -75.4854901487547$$
$$x_{89} = -5765.95698335107$$
$$x_{90} = -93.6369143694958$$
$$x_{91} = 94.1605131450941$$
$$x_{92} = -97.8257045742822$$
$$x_{93} = -60.1265927312047$$
$$x_{94} = -44.0695636128568$$