Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(2 x - 1 \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{1}{2}$$
$$x_{2} = \frac{1}{2} + \frac{\pi}{2}$$
Numerical solution$$x_{1} = 47.6238898038469$$
$$x_{2} = 2.0707963267949$$
$$x_{3} = -43.4822971502571$$
$$x_{4} = -63.9026493985908$$
$$x_{5} = -65.4734457253857$$
$$x_{6} = -78.0398163397448$$
$$x_{7} = -48.1946861306418$$
$$x_{8} = 58.6194640914112$$
$$x_{9} = -21.4911485751286$$
$$x_{10} = 74.3274273593601$$
$$x_{11} = 68.0442420521806$$
$$x_{12} = 91.606186954104$$
$$x_{13} = -32.4867228626928$$
$$x_{14} = -29.345130209103$$
$$x_{15} = 96.3185759344887$$
$$x_{16} = -41.9115008234622$$
$$x_{17} = 38.1991118430775$$
$$x_{18} = -100.030964914873$$
$$x_{19} = 80.6106126665397$$
$$x_{20} = 90.0353906273091$$
$$x_{21} = 72.7566310325652$$
$$x_{22} = -19.9203522483337$$
$$x_{23} = 39.7699081698724$$
$$x_{24} = -40.3407044966673$$
$$x_{25} = 14.6371669411541$$
$$x_{26} = -54.4778714378214$$
$$x_{27} = 22.4911485751286$$
$$x_{28} = 53.9070751110265$$
$$x_{29} = 17.7787595947439$$
$$x_{30} = -93.7477796076938$$
$$x_{31} = -12.0663706143592$$
$$x_{32} = 61.761056745001$$
$$x_{33} = -30.9159265358979$$
$$x_{34} = 75.898223686155$$
$$x_{35} = -5.78318530717959$$
$$x_{36} = 69.6150383789755$$
$$x_{37} = -73.3274273593601$$
$$x_{38} = -71.7566310325652$$
$$x_{39} = -13.6371669411541$$
$$x_{40} = 30.345130209103$$
$$x_{41} = -49.7654824574367$$
$$x_{42} = 52.3362787842316$$
$$x_{43} = 36.6283155162826$$
$$x_{44} = -98.4601685880785$$
$$x_{45} = 0.5$$
$$x_{46} = -57.6194640914112$$
$$x_{47} = 25.6327412287183$$
$$x_{48} = -76.4690200129499$$
$$x_{49} = -70.1858347057703$$
$$x_{50} = 44.4822971502571$$
$$x_{51} = -87.4645943005142$$
$$x_{52} = 11.4955742875643$$
$$x_{53} = 16.207963267949$$
$$x_{54} = 31.9159265358979$$
$$x_{55} = 97.8893722612836$$
$$x_{56} = -51.3362787842316$$
$$x_{57} = 50.7654824574367$$
$$x_{58} = -10.4955742875643$$
$$x_{59} = 33.4867228626928$$
$$x_{60} = -27.7743338823081$$
$$x_{61} = 3.64159265358979$$
$$x_{62} = 24.0619449019235$$
$$x_{63} = -26.2035375555132$$
$$x_{64} = 102.601761241668$$
$$x_{65} = -18.3495559215388$$
$$x_{66} = -85.8937979737193$$
$$x_{67} = -95.3185759344887$$
$$x_{68} = -7.35398163397448$$
$$x_{69} = -62.3318530717959$$
$$x_{70} = 8.35398163397448$$
$$x_{71} = 88.4645943005142$$
$$x_{72} = 82.1814089933346$$
$$x_{73} = 60.1902604182061$$
$$x_{74} = 55.4778714378214$$
$$x_{75} = 83.7522053201295$$
$$x_{76} = 9.92477796076938$$
$$x_{77} = -34.0575191894877$$
$$x_{78} = 94.7477796076938$$
$$x_{79} = -79.6106126665397$$
$$x_{80} = -92.1769832808989$$
$$x_{81} = 66.4734457253857$$
$$x_{82} = -35.6283155162826$$
$$x_{83} = -84.3230016469244$$
$$x_{84} = 46.053093477052$$
$$x_{85} = -56.0486677646163$$
$$x_{86} = -4.21238898038469$$