El gráfico de la función cruce el eje A con f = 0
o sea hay que resolver la ecuación:
$$\left(\sin{\left(4 a \right)} - \cos{\left(4 a \right)}\right) + \cos{\left(2 a \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje A:
Solución analítica$$a_{1} = 0$$
$$a_{2} = \pi$$
Solución numérica$$a_{1} = 34.0706943074751$$
$$a_{2} = -64.0611580490107$$
$$a_{3} = -13.795675591574$$
$$a_{4} = -39.9099728008373$$
$$a_{5} = -51.4947874346515$$
$$a_{6} = 96.1600672840687$$
$$a_{7} = -72.2566310325652$$
$$a_{8} = 84.3361767649118$$
$$a_{9} = 19.7802876173688$$
$$a_{10} = -59.6902604182061$$
$$a_{11} = 76.3289553819851$$
$$a_{12} = 80.4521040161198$$
$$a_{13} = 72.2566310325652$$
$$a_{14} = -2.21086095775973$$
$$a_{15} = 56.0618428826036$$
$$a_{16} = 10.3555096565994$$
$$a_{17} = 94.2477796076938$$
$$a_{18} = -57.7779727418311$$
$$a_{19} = -47.6107146858595$$
$$a_{20} = 4.07232434941985$$
$$a_{21} = 37.2122869610649$$
$$a_{22} = -87.9645943005142$$
$$a_{23} = 45.894584826632$$
$$a_{24} = -68.1843066831454$$
$$a_{25} = -3.62841753560244$$
$$a_{26} = 0$$
$$a_{27} = -17.9188242257087$$
$$a_{28} = 12.0795457323465$$
$$a_{29} = 100.044140032861$$
$$a_{30} = 50.2654824574367$$
$$a_{31} = -31.9027514179106$$
$$a_{32} = 48.054621499677$$
$$a_{33} = -35.7868241667026$$
$$a_{34} = 70.0457700748055$$
$$a_{35} = 14.4786582907341$$
$$a_{36} = -79.7691213169597$$
$$a_{37} = 30.1866215586831$$
$$a_{38} = 85.7537333427545$$
$$a_{39} = -21.9911485751286$$
$$a_{40} = -7.51249028439444$$
$$a_{41} = 36.4698068658627$$
$$a_{42} = 23.9034362515035$$
$$a_{43} = 78.0529914577322$$
$$a_{44} = 59.2034355361934$$
$$a_{45} = -83.8922699510944$$
$$a_{46} = 87.9645943005142$$
$$a_{47} = 52.1777701338116$$
$$a_{48} = -61.9011213759658$$
$$a_{49} = -29.503638859523$$
$$a_{50} = -77.6090846439148$$
$$a_{51} = 32.346658231728$$
$$a_{52} = -46.1931581080168$$
$$a_{53} = 15.2211383859363$$
$$a_{54} = -43.9822971502571$$
$$a_{55} = -37.6991118430775$$
$$a_{56} = -65.9734457253857$$
$$a_{57} = 41.7714361924974$$
$$a_{58} = 63.7625847676259$$
$$a_{59} = 6.28318530717959$$
$$a_{60} = 89.8768819768892$$
$$a_{61} = 28.2743338823081$$
$$a_{62} = -91.5930118361167$$
$$a_{63} = 8.19547298355452$$
$$a_{64} = -6.77001018919224$$
$$a_{65} = -94.2477796076938$$
$$a_{66} = -99.6002332190433$$
$$a_{67} = -24.2020095328883$$
$$a_{68} = -33.6267874936577$$
$$a_{69} = -25.619566110731$$
$$a_{70} = 43.9822971502571$$
$$a_{71} = 40.3538796146547$$
$$a_{72} = 54.3378068068565$$
$$a_{73} = 65.9734457253857$$
$$a_{74} = 18.3627310395261$$
$$a_{75} = -11.6356389185291$$
$$a_{76} = -15.707963267949$$
$$a_{77} = -50.2654824574367$$
$$a_{78} = -90.1754552582739$$
$$a_{79} = 26.0634729245484$$
$$a_{80} = 62.3450281897832$$
$$a_{81} = -20.0788608987536$$
$$a_{82} = 58.4609554409912$$
$$a_{83} = -55.6179360687862$$
$$a_{84} = -95.4770845849087$$
$$a_{85} = -9.91160284278203$$
$$a_{86} = 98.3201039571136$$
$$a_{87} = 74.1689187089402$$
$$a_{88} = 21.9911485751286$$
$$a_{89} = -86.0523066241393$$
$$a_{90} = -42.0700094738822$$
$$a_{91} = -73.4859360097801$$
$$a_{92} = 1.91228767637494$$
$$a_{93} = -28.2743338823081$$
$$a_{94} = 67.8857334017606$$
$$a_{95} = -97.8761971432962$$
$$a_{96} = 92.0369186499341$$
$$a_{97} = -69.6018632609881$$
$$a_{98} = -53.8938999930391$$
$$a_{99} = -81.6814089933346$$
$$a_{100} = -75.8850485681677$$