El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\log{\left(\sqrt{2} \sin{\left(x + 1 \right)} \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = -1 + \frac{\pi}{4}$$
$$x_{2} = -1 + \frac{3 \pi}{4}$$
Solución numérica$$x_{1} = 37.484510006475$$
$$x_{2} = -50.4800842940392$$
$$x_{3} = -48.9092879672443$$
$$x_{4} = 70.4712328691678$$
$$x_{5} = 87.7499924639117$$
$$x_{6} = 32.7721210260903$$
$$x_{7} = -86.6083998103219$$
$$x_{8} = -61.4756585816035$$
$$x_{9} = 89.3207887907066$$
$$x_{10} = 68.9004365423729$$
$$x_{11} = 13.9225651045515$$
$$x_{12} = 45.3384916404494$$
$$x_{13} = 31.2013246992954$$
$$x_{14} = 1.35619449019234$$
$$x_{15} = -74.0420291959627$$
$$x_{16} = -11.2101761241668$$
$$x_{17} = 12.3517687777566$$
$$x_{18} = -56.7632696012188$$
$$x_{19} = 43.7676953136546$$
$$x_{20} = -42.6261026600648$$
$$x_{21} = -6.49778714378214$$
$$x_{22} = -69.329640215578$$
$$x_{23} = 57.9048622548086$$
$$x_{24} = 95.6039740978861$$
$$x_{25} = 7.63937979737193$$
$$x_{26} = -80.3252145031423$$
$$x_{27} = 101.887159405066$$
$$x_{28} = -75.6128255227576$$
$$x_{29} = -37.9137136796801$$
$$x_{30} = -55.1924732744239$$
$$x_{31} = 83.037603483527$$
$$x_{32} = 18.6349540849362$$
$$x_{33} = 100.316363078271$$
$$x_{34} = -36.3429173528852$$
$$x_{35} = -88.1791961371168$$
$$x_{36} = -44.1968989868597$$
$$x_{37} = 56.3340659280137$$
$$x_{38} = -63.0464549083984$$
$$x_{39} = -12.7809724509617$$
$$x_{40} = -92.8915851175014$$
$$x_{41} = 6.06858347057703$$
$$x_{42} = 39.0553063332699$$
$$x_{43} = -17.4933614313464$$
$$x_{44} = -0.214601836602552$$
$$x_{45} = -31.6305283725005$$
$$x_{46} = 51.621676947629$$
$$x_{47} = -30.0597320457056$$
$$x_{48} = 75.1836218495525$$
$$x_{49} = 24.9181393921158$$
$$x_{50} = 76.7544181763474$$
$$x_{51} = -99.174770424681$$
$$x_{52} = -25.3473430653209$$
$$x_{53} = -81.8960108299372$$
$$x_{54} = -19.0641577581413$$
$$x_{55} = 81.4668071567321$$
$$x_{56} = -4.92699081698724$$
$$x_{57} = 26.4889357189107$$
$$x_{58} = 64.1880475619882$$
$$x_{59} = -94.4623814442964$$
$$x_{60} = 62.6172512351933$$
$$x_{61} = -67.7588438887831$$
$$x_{62} = 50.0508806208341$$
$$x_{63} = -23.776546738526$$
$$x_{64} = 20.2057504117311$$
$$x_{65} = 94.0331777710912$$