El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$- 2 \sin{\left(4 x + \frac{4 \pi}{3} \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\pi}{12}$$
$$x_{2} = \frac{\pi}{6}$$
Solución numérica$$x_{1} = 64.1408500107916$$
$$x_{2} = 92.4151838930998$$
$$x_{3} = -13.6135681655558$$
$$x_{4} = 96.342174710087$$
$$x_{5} = -92.1533845053006$$
$$x_{6} = -59.9520598060052$$
$$x_{7} = 56.2868683768171$$
$$x_{8} = -23.8237442897226$$
$$x_{9} = -48.1710873550435$$
$$x_{10} = -57.5958653158129$$
$$x_{11} = 6.02138591938044$$
$$x_{12} = 50.0036830696375$$
$$x_{13} = 42.1497014356631$$
$$x_{14} = -37.9609112308767$$
$$x_{15} = 8.37758040957278$$
$$x_{16} = -8.11578102177363$$
$$x_{17} = -5.75958653158129$$
$$x_{18} = 93.9859802198946$$
$$x_{19} = 79.8488132787406$$
$$x_{20} = -19.8967534727354$$
$$x_{21} = -38.7463093942741$$
$$x_{22} = 48.4328867428426$$
$$x_{23} = 70.4240353179712$$
$$x_{24} = -41.8879020478639$$
$$x_{25} = -35.6047167406843$$
$$x_{26} = 71.9948316447661$$
$$x_{27} = 97.9129710368819$$
$$x_{28} = 78.2780169519457$$
$$x_{29} = -31.6777259236971$$
$$x_{30} = 35.8665161284835$$
$$x_{31} = -30.1069295969022$$
$$x_{32} = 20.1585528605345$$
$$x_{33} = 28.012534494509$$
$$x_{34} = 68.8532389911763$$
$$x_{35} = 75.9218224617533$$
$$x_{36} = -93.7241808320955$$
$$x_{37} = 13.8753675533549$$
$$x_{38} = 52.3598775598299$$
$$x_{39} = -53.6688744988256$$
$$x_{40} = -67.8060414399797$$
$$x_{41} = -74.0892267471593$$
$$x_{42} = 17.8023583703422$$
$$x_{43} = -34.0339204138894$$
$$x_{44} = -89.7971900151083$$
$$x_{45} = -63.8790506229925$$
$$x_{46} = 82.2050077689329$$
$$x_{47} = 9.94837673636768$$
$$x_{48} = 60.2138591938044$$
$$x_{49} = 31.9395253114962$$
$$x_{50} = -49.7418836818384$$
$$x_{51} = 24.0855436775217$$
$$x_{52} = 2.0943951023932$$
$$x_{53} = 60.9992573572018$$
$$x_{54} = -97.6511716490827$$
$$x_{55} = 38.2227106186758$$
$$x_{56} = -1.83259571459405$$
$$x_{57} = -81.9432083811338$$
$$x_{58} = 74.3510261349584$$
$$x_{59} = 53.9306738866248$$
$$x_{60} = -45.8148928648512$$
$$x_{61} = -26.1799387799149$$
$$x_{62} = 46.0766922526503$$
$$x_{63} = -15.9697626557481$$
$$x_{64} = -56.025068989018$$
$$x_{65} = 4.45058959258554$$
$$x_{66} = 100.269165527074$$
$$x_{67} = 30.3687289847013$$
$$x_{68} = 68.0678408277789$$
$$x_{69} = 26.4417381677141$$
$$x_{70} = 16.2315620435473$$
$$x_{71} = -78.0162175641465$$
$$x_{72} = -79.5870138909414$$
$$x_{73} = -85.870199198121$$
$$x_{74} = -12.0427718387609$$
$$x_{75} = -75.6600230739542$$
$$x_{76} = 86.1319985859202$$
$$x_{77} = -45.0294947014537$$
$$x_{78} = 57.857664703612$$
$$x_{79} = 12.30457122656$$
$$x_{80} = -9.68657734856853$$
$$x_{81} = -100.007366139275$$
$$x_{82} = 90.0589894029074$$
$$x_{83} = -71.733032256967$$
$$x_{84} = -27.7507351067098$$
$$x_{85} = -25.3945406165175$$
$$x_{86} = -96.0803753222878$$
$$x_{87} = -52.0980781720307$$
$$x_{88} = 31.1541271480988$$
$$x_{89} = -4.18879020478639$$
$$x_{90} = -16.7551608191456$$
$$x_{91} = 34.2957198016886$$
$$x_{92} = -70.162235930172$$