El gráfico de la función cruce el eje T con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(3 t \right)} \cos{\left(t \right)} + \cos^{2}{\left(5 t \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje T:
Solución numérica$$t_{1} = 1.5707963267949$$
$$t_{2} = -7.06858347057703$$
$$t_{3} = -81.8453258326253$$
$$t_{4} = 18.3006069564618$$
$$t_{5} = -16.7070104388889$$
$$t_{6} = 32.9867228626928$$
$$t_{7} = -85.8220488178644$$
$$t_{8} = -59.8541772574967$$
$$t_{9} = 6.11926846788891$$
$$t_{10} = -29.0597320457056$$
$$t_{11} = 71.2575838616253$$
$$t_{12} = 49.4800842940392$$
$$t_{13} = 61.2208185498598$$
$$t_{14} = -69.9004365423729$$
$$t_{15} = 92.6769832808989$$
$$t_{16} = 72.0927141932746$$
$$t_{17} = -32.9867228626928$$
$$t_{18} = 23.5619449019235$$
$$t_{19} = -91.8915851175014$$
$$t_{20} = -9.97372692584633$$
$$t_{21} = 84.2740526818475$$
$$t_{22} = 90.5572379890271$$
$$t_{23} = -37.8630286823682$$
$$t_{24} = 77.7544181763474$$
$$t_{25} = 59.1413114531291$$
$$t_{26} = 8.63937979737193$$
$$t_{27} = 94.0838627684031$$
$$t_{28} = -51.2645296283766$$
$$t_{29} = 17.2385213996027$$
$$t_{30} = -73.2556782035052$$
$$t_{31} = 34.0085702244108$$
$$t_{32} = -4.14063982452974$$
$$t_{33} = -80.1106126665397$$
$$t_{34} = -19.8486030924787$$
$$t_{35} = -41.8397516676073$$
$$t_{36} = -125.827622982882$$
$$t_{37} = 90.3207887907066$$
$$t_{38} = -58.1597022865523$$
$$t_{39} = 55.5496205936763$$
$$t_{40} = -76.9690200129499$$
$$t_{41} = 45.5128552819108$$
$$t_{42} = 2.97767581429912$$
$$t_{43} = -53.9560240761034$$
$$t_{44} = 81.1324600282577$$
$$t_{45} = 86.3937979737193$$
$$t_{46} = -97.9383212263605$$
$$t_{47} = 2.14254548264985$$
$$t_{48} = -60.239209383283$$
$$t_{49} = 40.0553063332699$$
$$t_{50} = -25.9181393921158$$
$$t_{51} = -39.3101463650136$$
$$t_{52} = 50.101565618146$$
$$t_{53} = 491.659250286803$$
$$t_{54} = 65.1880475619882$$
$$t_{55} = 77.9908673746679$$
$$t_{56} = -36.1685537114238$$
$$t_{57} = 24.1336940577784$$
$$t_{58} = -14.1774051362952$$
$$t_{59} = -31.9648755009749$$
$$t_{60} = -29.8853684042442$$
$$t_{61} = -13.1153195794361$$
$$t_{62} = -75.947172651232$$
$$t_{63} = 12.0174216492822$$
$$t_{64} = -95.8185759344887$$
$$t_{65} = 58.9048622548086$$
$$t_{66} = 43.1968989868597$$
$$t_{67} = -4.75262717552585$$
$$t_{68} = -0.999047170939943$$
$$t_{69} = 68.1159912080355$$
$$t_{70} = 96.3903250903437$$
$$t_{71} = -95.0331777710912$$
$$t_{72} = 36.9137136796801$$
$$t_{73} = 28.1104170430175$$
$$t_{74} = -69.2789552182661$$
$$t_{75} = 7.81374343883332$$
$$t_{76} = 55.9997187995393$$
$$t_{77} = -63.6172512351933$$
$$t_{78} = 62.2829041067189$$
$$t_{79} = 99.9820159497964$$
$$t_{80} = -73.8274273593601$$
$$t_{81} = 14.9225651045515$$
$$t_{82} = 191.473235029687$$
$$t_{83} = -47.9092879672443$$
$$t_{84} = -15.8718801072396$$
$$t_{85} = -63.8309002427358$$