El gráfico de la función cruce el eje A con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(3 a \right)} + \cos{\left(a \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje A:
Solución analítica$$a_{1} = - \frac{5 \pi}{8}$$
$$a_{2} = - \frac{\pi}{4}$$
$$a_{3} = - \frac{\pi}{8}$$
$$a_{4} = \frac{3 \pi}{8}$$
$$a_{5} = \frac{3 \pi}{4}$$
$$a_{6} = \frac{7 \pi}{8}$$
Solución numérica$$a_{1} = -8.24668071567321$$
$$a_{2} = -33.3794219443916$$
$$a_{3} = -82.0741080750334$$
$$a_{4} = -25.9181393921158$$
$$a_{5} = -45.9457925587507$$
$$a_{6} = -99.3528676697772$$
$$a_{7} = 96.6039740978861$$
$$a_{8} = -31.8086256175967$$
$$a_{9} = 13.7444678594553$$
$$a_{10} = -1.96349540849362$$
$$a_{11} = 10.6028752058656$$
$$a_{12} = 76.5763209312512$$
$$a_{13} = 12.1736715326604$$
$$a_{14} = -34.9502182711865$$
$$a_{15} = -96.2112750161874$$
$$a_{16} = -66.3661448070844$$
$$a_{17} = -11.388273369263$$
$$a_{18} = 70.2931356240716$$
$$a_{19} = -44.3749962319558$$
$$a_{20} = 92.2842841992002$$
$$a_{21} = 5.89048622548086$$
$$a_{22} = 98.5674695063798$$
$$a_{23} = 93.8550805259951$$
$$a_{24} = 67.1515429704818$$
$$a_{25} = 74.6128255227576$$
$$a_{26} = 68.329640215578$$
$$a_{27} = 54.5851723561227$$
$$a_{28} = -85.6083998103219$$
$$a_{29} = -0.392699081698724$$
$$a_{30} = 65.5807466436869$$
$$a_{31} = -56.941366846315$$
$$a_{32} = -3.92699081698724$$
$$a_{33} = 49.872783375738$$
$$a_{34} = -22.3838476568273$$
$$a_{35} = 90.3207887907066$$
$$a_{36} = -52.2289778659303$$
$$a_{37} = 56.1559686829176$$
$$a_{38} = -41.6261026600648$$
$$a_{39} = 20.0276531666349$$
$$a_{40} = 53.0143760293278$$
$$a_{41} = 87.5718952188155$$
$$a_{42} = -97.7820713429823$$
$$a_{43} = -61.6537558266997$$
$$a_{44} = -19.6349540849362$$
$$a_{45} = -47.9092879672443$$
$$a_{46} = 24.3473430653209$$
$$a_{47} = 26.3108384738145$$
$$a_{48} = 71.8639319508665$$
$$a_{49} = -12.9590696960579$$
$$a_{50} = -39.6626072515711$$
$$a_{51} = 35.7356164345839$$
$$a_{52} = 32.5940237809941$$
$$a_{53} = 27.8816348006094$$
$$a_{54} = -16.1006623496477$$
$$a_{55} = -38.0918109247762$$
$$a_{56} = -98.174770424681$$
$$a_{57} = -53.7997741927252$$
$$a_{58} = -17.6714586764426$$
$$a_{59} = 64.009950316892$$
$$a_{60} = 42.0188017417635$$
$$a_{61} = -74.2201264410589$$
$$a_{62} = 84.037603483527$$
$$a_{63} = -89.9280897090078$$
$$a_{64} = -67.9369411338793$$
$$a_{65} = 4.31968989868597$$
$$a_{66} = -77.3617190946487$$
$$a_{67} = 86.0010988920206$$
$$a_{68} = 48.3019870489431$$
$$a_{69} = -69.9004365423729$$
$$a_{70} = 21.5984494934298$$
$$a_{71} = 52.621676947629$$
$$a_{72} = 9.03207887907065$$
$$a_{73} = -30.2378292908018$$
$$a_{74} = -88.3572933822129$$
$$a_{75} = 33.7721210260903$$
$$a_{76} = 46.3384916404494$$
$$a_{77} = -60.0829594999048$$
$$a_{78} = -63.6172512351933$$
$$a_{79} = -91.8915851175014$$
$$a_{80} = 2.35619449019234$$
$$a_{81} = 57.7267650097125$$
$$a_{82} = 40.0553063332699$$
$$a_{83} = 30.6305283725005$$
$$a_{84} = -75.7909227678538$$
$$a_{85} = 79.717913584841$$
$$a_{86} = -9.8174770424681$$
$$a_{87} = 18.0641577581413$$
$$a_{88} = 43.5895980685584$$
$$a_{89} = 34.164820107789$$
$$a_{90} = 100.138265833175$$
$$a_{91} = 78.1471172580461$$
$$a_{92} = -23.9546439836222$$
$$a_{93} = 62.0464549083984$$
$$a_{94} = -55.3705705195201$$
$$a_{95} = -7.06858347057703$$
$$a_{96} = -78.9325154214436$$
$$a_{97} = -83.6449044018282$$