El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(5 x \right)} + \frac{\cos{\left(\pi \right)}}{3} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\operatorname{asin}{\left(\frac{1}{3} \right)}}{5} + \frac{\pi}{5}$$
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{1}{3} \right)}}{5}$$
Solución numérica$$x_{1} = 84.2626504980973$$
$$x_{2} = -20.0382256010839$$
$$x_{3} = 8.10017351744264$$
$$x_{4} = -5.72283415835245$$
$$x_{5} = 65.9054783434948$$
$$x_{6} = -38.3953977556863$$
$$x_{7} = -22.0591159570194$$
$$x_{8} = -91.6665381029311$$
$$x_{9} = -15.7759306498398$$
$$x_{10} = -35.8821236328145$$
$$x_{11} = 74.2095540066099$$
$$x_{12} = -93.6874284588667$$
$$x_{13} = 0.0679673818908244$$
$$x_{14} = -32.1122124485067$$
$$x_{15} = -86.1476060902512$$
$$x_{16} = -42.1653089399941$$
$$x_{17} = -87.8966269186234$$
$$x_{18} = 33.9971680406606$$
$$x_{19} = -25.8290271413271$$
$$x_{20} = -89.9175172745589$$
$$x_{21} = 75.9585748349822$$
$$x_{22} = 88.032561682405$$
$$x_{23} = -71.0679613530202$$
$$x_{24} = 48.312559483392$$
$$x_{25} = 96.0647678179568$$
$$x_{26} = 21.9231811932377$$
$$x_{27} = -76.0945095987638$$
$$x_{28} = -1.9529229740447$$
$$x_{29} = 23.9440715491733$$
$$x_{30} = -17.0325677112757$$
$$x_{31} = -69.8113242915842$$
$$x_{32} = 92.2948566336491$$
$$x_{33} = 52.0824706676997$$
$$x_{34} = 70.9320265892385$$
$$x_{35} = 72.1886636506744$$
$$x_{36} = 44.0502645321479$$
$$x_{37} = 82.2417601421618$$
$$x_{38} = -12.006019465532$$
$$x_{39} = -99.9706137660463$$
$$x_{40} = 55.8523818520075$$
$$x_{41} = 83.4983972035977$$
$$x_{42} = 18.15327000893$$
$$x_{43} = 99.8346790022646$$
$$x_{44} = 54.1033610236353$$
$$x_{45} = -9.98512910959651$$
$$x_{46} = 10.1210638733782$$
$$x_{47} = -13.7550402939043$$
$$x_{48} = 26459.8179329766$$
$$x_{49} = 42.0293741762124$$
$$x_{50} = 64.1564575151226$$
$$x_{51} = 31.9762776847251$$
$$x_{52} = -33.8612332768789$$
$$x_{53} = 45.3069015935838$$
$$x_{54} = -97.9497234101107$$
$$x_{55} = 49.5691965448279$$
$$x_{56} = 94.3157469895846$$
$$x_{57} = -37.6311444611867$$
$$x_{58} = 11.8700847017504$$
$$x_{59} = -96.6930863486748$$
$$x_{60} = 86.0116713264695$$
$$x_{61} = 67.9263686994304$$
$$x_{62} = -66.0414131072765$$
$$x_{63} = 60.3865463308149$$
$$x_{64} = -58.501590738661$$
$$x_{65} = -47.684240952674$$
$$x_{66} = 38.2594629919047$$
$$x_{67} = -59.7582278000969$$
$$x_{68} = -49.7051313086096$$
$$x_{69} = 1.81698821026305$$
$$x_{70} = 30.2272568563528$$
$$x_{71} = -81.6134416114438$$
$$x_{72} = -79.8644207830716$$
$$x_{73} = -77.843530427136$$
$$x_{74} = 16.4042491805577$$
$$x_{75} = -45.9352201243018$$
$$x_{76} = -43.9143297683663$$
$$x_{77} = 6.35115268907041$$
$$x_{78} = 77.9794651909177$$
$$x_{79} = 4.33026233313489$$
$$x_{80} = -57.7373374441614$$
$$x_{81} = 98.0856581738924$$
$$x_{82} = 20.1741603648655$$
$$x_{83} = 62.1355671591871$$
$$x_{84} = -27.5780479696994$$
$$x_{85} = 28.9706197949169$$
$$x_{86} = -15.0116773553402$$
$$x_{87} = -30.0913220925712$$
$$x_{88} = -67.7904339356487$$
$$x_{89} = -53.9674262598536$$
$$x_{90} = -74.0736192428283$$
$$x_{91} = -120.076806749021$$
$$x_{92} = -3.70194380241693$$
$$x_{93} = 28.2063665004173$$
$$x_{94} = 40.2803533478402$$
$$x_{95} = 50.3334498393275$$
$$x_{96} = -55.9883166157891$$
$$x_{97} = -64.020522751341$$
$$x_{98} = -23.8081367853916$$