El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$8 \sin^{2}{\left(7 x \right)} - 3 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\operatorname{asin}{\left(\frac{\sqrt{6}}{4} \right)}}{7} + \frac{\pi}{7}$$
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{\sqrt{6}}{4} \right)}}{7} + \frac{\pi}{7}$$
$$x_{3} = - \frac{\operatorname{asin}{\left(\frac{\sqrt{6}}{4} \right)}}{7}$$
$$x_{4} = \frac{\operatorname{asin}{\left(\frac{\sqrt{6}}{4} \right)}}{7}$$
Solución numérica$$x_{1} = 52.1548294074632$$
$$x_{2} = 66.0675968733609$$
$$x_{3} = -69.9184851320259$$
$$x_{4} = 4.13334170259065$$
$$x_{5} = 34.6516703374629$$
$$x_{6} = -43.8881460022819$$
$$x_{7} = -77.7363695866944$$
$$x_{8} = -83.8312525979236$$
$$x_{9} = 16.250913366437$$
$$x_{10} = -29.7148818818218$$
$$x_{11} = -97.7440200638212$$
$$x_{12} = -35.9980671890014$$
$$x_{13} = 22.0852997231038$$
$$x_{14} = -27.7313837838201$$
$$x_{15} = -45.8716441002836$$
$$x_{16} = 44.0764482982323$$
$$x_{17} = -54.2105218640769$$
$$x_{18} = 14.2674152684353$$
$$x_{19} = 50.1713313094615$$
$$x_{20} = -67.8627926754122$$
$$x_{21} = 24.1409921797175$$
$$x_{22} = -41.8324535456682$$
$$x_{23} = -37.7932629910527$$
$$x_{24} = 83.8312525979236$$
$$x_{25} = -14.0069186138729$$
$$x_{26} = 26.1244902777192$$
$$x_{27} = 32.2193732889484$$
$$x_{28} = -19.8413049705396$$
$$x_{29} = -1.25224570356328$$
$$x_{30} = 38.2420619415655$$
$$x_{31} = 74.1459779825918$$
$$x_{32} = 98.192819014334$$
$$x_{33} = 80.2408609938209$$
$$x_{34} = 67.6744903794618$$
$$x_{35} = -17.8578068725379$$
$$x_{36} = 70.1067874279763$$
$$x_{37} = 92.0979360031049$$
$$x_{38} = -23.4316965746422$$
$$x_{39} = -39.8489554476665$$
$$x_{40} = 84.2800515484364$$
$$x_{41} = -75.7528714886927$$
$$x_{42} = -99.7275181618229$$
$$x_{43} = -33.7540724364373$$
$$x_{44} = 60.2332105166941$$
$$x_{45} = 58.2497124186924$$
$$x_{46} = 30.1636808323347$$
$$x_{47} = -63.8236021207967$$
$$x_{48} = 28.1801827343329$$
$$x_{49} = -61.840104022795$$
$$x_{50} = -81.7755601413098$$
$$x_{51} = -11.7629238613087$$
$$x_{52} = -65.8792945774105$$
$$x_{53} = 11.7629238613087$$
$$x_{54} = 20.2901039210524$$
$$x_{55} = 62.4772052692582$$
$$x_{56} = 0.0941511479752013$$
$$x_{57} = -47.9273365568974$$
$$x_{58} = -91.649137052592$$
$$x_{59} = -21.8969974271534$$
$$x_{60} = -85.8147506959253$$
$$x_{61} = -49.7225323589487$$
$$x_{62} = -59.7844115661813$$
$$x_{63} = -80.2408609938209$$
$$x_{64} = -15.8021144159242$$
$$x_{65} = 2.14984360458894$$
$$x_{66} = 77.9968662412568$$
$$x_{67} = 64.2724010713095$$
$$x_{68} = 10.2282247138198$$
$$x_{69} = 94.1536284597186$$
$$x_{70} = -5.74023520869156$$
$$x_{71} = -87.870443152539$$
$$x_{72} = -53.7617229135641$$
$$x_{73} = 6.18903415920439$$
$$x_{74} = 42.281252496181$$
$$x_{75} = -89.8539412505407$$
$$x_{76} = 86.2635496464381$$
$$x_{77} = 33.3052734859244$$
$$x_{78} = -91.9096337071545$$
$$x_{79} = -31.5100776838731$$
$$x_{80} = 48.1156388528478$$
$$x_{81} = -7.72373330669327$$
$$x_{82} = 54.2105218640769$$
$$x_{83} = 76.2016704392055$$
$$x_{84} = -71.7136809340772$$
$$x_{85} = 84.4683538443868$$
$$x_{86} = 46.132140754846$$
$$x_{87} = 72.16247988459$$
$$x_{88} = 96.1371265577203$$