Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(8 x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{8}$$
Numerical solution$$x_{1} = -43.9822971502571$$
$$x_{2} = -29.845130209103$$
$$x_{3} = -79.717913584841$$
$$x_{4} = -25.9181393921158$$
$$x_{5} = -45.9457925587507$$
$$x_{6} = -84.037603483527$$
$$x_{7} = 28.2743338823081$$
$$x_{8} = -86.0010988920206$$
$$x_{9} = -15.707963267949$$
$$x_{10} = -55.7632696012188$$
$$x_{11} = 72.2566310325652$$
$$x_{12} = -31.8086256175967$$
$$x_{13} = 45.553093477052$$
$$x_{14} = -1.96349540849362$$
$$x_{15} = 12.1736715326604$$
$$x_{16} = -13.7444678594553$$
$$x_{17} = 1.96349540849362$$
$$x_{18} = -11.7809724509617$$
$$x_{19} = -21.9911485751286$$
$$x_{20} = -57.7267650097125$$
$$x_{21} = 76.1836218495525$$
$$x_{22} = 70.2931356240716$$
$$x_{23} = -77.7544181763474$$
$$x_{24} = 92.2842841992002$$
$$x_{25} = -60.8683576633022$$
$$x_{26} = 74.2201264410589$$
$$x_{27} = 32.2013246992954$$
$$x_{28} = 50.2654824574367$$
$$x_{29} = 67.1515429704818$$
$$x_{30} = 23.9546439836222$$
$$x_{31} = -42.0188017417635$$
$$x_{32} = -3.92699081698724$$
$$x_{33} = 30.2378292908018$$
$$x_{34} = 60.0829594999048$$
$$x_{35} = 56.1559686829176$$
$$x_{36} = -64.009950316892$$
$$x_{37} = -5.89048622548086$$
$$x_{38} = 52.2289778659303$$
$$x_{39} = 20.0276531666349$$
$$x_{40} = -87.9645943005142$$
$$x_{41} = -62.0464549083984$$
$$x_{42} = -34.5575191894877$$
$$x_{43} = -97.7820713429823$$
$$x_{44} = 48.6946861306418$$
$$x_{45} = 0$$
$$x_{46} = -47.9092879672443$$
$$x_{47} = -20.0276531666349$$
$$x_{48} = -65.9734457253857$$
$$x_{49} = -73.8274273593601$$
$$x_{50} = 6.28318530717959$$
$$x_{51} = 94.2477796076938$$
$$x_{52} = 54.1924732744239$$
$$x_{53} = 65.9734457253857$$
$$x_{54} = 36.1283155162826$$
$$x_{55} = 16.1006623496477$$
$$x_{56} = -99.7455667514759$$
$$x_{57} = -53.7997741927252$$
$$x_{58} = -71.8639319508665$$
$$x_{59} = 27.4889357189107$$
$$x_{60} = 21.9911485751286$$
$$x_{61} = 64.009950316892$$
$$x_{62} = 111.919238284136$$
$$x_{63} = 42.0188017417635$$
$$x_{64} = 8.24668071567321$$
$$x_{65} = -27.8816348006094$$
$$x_{66} = 14.1371669411541$$
$$x_{67} = 84.037603483527$$
$$x_{68} = 87.9645943005142$$
$$x_{69} = -89.9280897090078$$
$$x_{70} = -67.9369411338793$$
$$x_{71} = -37.6991118430775$$
$$x_{72} = -51.8362787842316$$
$$x_{73} = 10.2101761241668$$
$$x_{74} = 86.0010988920206$$
$$x_{75} = -69.9004365423729$$
$$x_{76} = -33.7721210260903$$
$$x_{77} = -49.872783375738$$
$$x_{78} = 9.8174770424681$$
$$x_{79} = -35.7356164345839$$
$$x_{80} = 43.9822971502571$$
$$x_{81} = 82.0741080750334$$
$$x_{82} = -95.8185759344887$$
$$x_{83} = 80.1106126665397$$
$$x_{84} = -91.8915851175014$$
$$x_{85} = -7.85398163397448$$
$$x_{86} = 40.0553063332699$$
$$x_{87} = -93.8550805259951$$
$$x_{88} = -75.7909227678538$$
$$x_{89} = -9.8174770424681$$
$$x_{90} = 98.174770424681$$
$$x_{91} = 18.0641577581413$$
$$x_{92} = 34.164820107789$$
$$x_{93} = 100.138265833175$$
$$x_{94} = 78.1471172580461$$
$$x_{95} = -23.9546439836222$$
$$x_{96} = 62.0464549083984$$
$$x_{97} = 38.0918109247762$$
$$x_{98} = 58.1194640914112$$
$$x_{99} = 96.2112750161874$$
$$x_{100} = -31.4159265358979$$