El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$2 \sin{\left(2 x + \frac{1}{2} \right)} - \frac{1}{2} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{1}{4} + \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{2}$$
$$x_{2} = - \frac{1}{4} - \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{2} + \frac{\pi}{2}$$
Solución numérica$$x_{1} = 86.0174578461483$$
$$x_{2} = 65.8497858529567$$
$$x_{3} = 43.8586372778281$$
$$x_{4} = 56.4250078921873$$
$$x_{5} = -9.54843783319834$$
$$x_{6} = 35.7519753887116$$
$$x_{7} = -11.3719144151353$$
$$x_{8} = 79.7342725389687$$
$$x_{9} = 12.4427107419302$$
$$x_{10} = -97.5130321337126$$
$$x_{11} = 37.5754519706486$$
$$x_{12} = -55.3542115653924$$
$$x_{13} = 78.4161564673159$$
$$x_{14} = -25.2564011011473$$
$$x_{15} = -39.6462482974435$$
$$x_{16} = 76.5926798853789$$
$$x_{17} = -31.5395864083269$$
$$x_{18} = 32.6103827351218$$
$$x_{19} = -8.23032176154552$$
$$x_{20} = -52.2126189118026$$
$$x_{21} = -91.229846826533$$
$$x_{22} = -23.9382850294945$$
$$x_{23} = -80.4869527941108$$
$$x_{24} = 57.7431239638401$$
$$x_{25} = -45.929433604623$$
$$x_{26} = 31.292266663469$$
$$x_{27} = 40.7170446242384$$
$$x_{28} = -67.9205821797516$$
$$x_{29} = -66.0971055978146$$
$$x_{30} = 239.955497872048$$
$$x_{31} = 28.1506740098792$$
$$x_{32} = 15.58430339552$$
$$x_{33} = 51.4599386566605$$
$$x_{34} = 23.1856047743524$$
$$x_{35} = -1.94713645436594$$
$$x_{36} = 29.468790081532$$
$$x_{37} = -77.345360140521$$
$$x_{38} = 59.5666005457771$$
$$x_{39} = 100.407305042444$$
$$x_{40} = -94.3714394801228$$
$$x_{41} = 13.760826813583$$
$$x_{42} = 4.33604885281365$$
$$x_{43} = -88.0882541729432$$
$$x_{44} = -3.26525252601875$$
$$x_{45} = 64.0263092710197$$
$$x_{46} = 84.6993417744955$$
$$x_{47} = -96.1949160620597$$
$$x_{48} = 42.0351606958912$$
$$x_{49} = 62.7081931993669$$
$$x_{50} = 26.3271974279422$$
$$x_{51} = -33.3630629902639$$
$$x_{52} = -30.2214703366741$$
$$x_{53} = -22.1148084475575$$
$$x_{54} = -99.3365087156495$$
$$x_{55} = -36.5046556438537$$
$$x_{56} = 6.15952543475063$$
$$x_{57} = -17.6550997223149$$
$$x_{58} = 73.4510872317891$$
$$x_{59} = 21.8674887026996$$
$$x_{60} = -74.2037674869312$$
$$x_{61} = 48.3183460030708$$
$$x_{62} = 72.1329711601363$$
$$x_{63} = -37.8227717155065$$
$$x_{64} = -28.3979937547371$$
$$x_{65} = -89.9117307548802$$
$$x_{66} = -72.3802909049942$$
$$x_{67} = 18.7258960491098$$
$$x_{68} = -14.5135070687251$$
$$x_{69} = -6.40684517960855$$
$$x_{70} = 92.3006431533279$$
$$x_{71} = -15.8316231403779$$
$$x_{72} = 20.0440121207626$$
$$x_{73} = -59.813920290635$$
$$x_{74} = 95.4422358069177$$
$$x_{75} = -50.3891423298656$$
$$x_{76} = -75.521883558584$$
$$x_{77} = -58.4958042189822$$
$$x_{78} = -53.5307349834554$$
$$x_{79} = 7.47764150640344$$
$$x_{80} = 98.5838284605074$$
$$x_{81} = 10.6192341599932$$
$$x_{82} = -81.8050688657636$$
$$x_{83} = -0.123659872428961$$
$$x_{84} = -69.2386982514044$$
$$x_{85} = -61.637396872572$$
$$x_{86} = -44.1059570226861$$
$$x_{87} = -47.2475496762759$$
$$x_{88} = -363.230291617192$$
$$x_{89} = 54.6015313102503$$
$$x_{90} = 70.3094945781993$$
$$x_{91} = 94.1241197352648$$
$$x_{92} = 87.8409344280852$$
$$x_{93} = 34.4338593170588$$
$$x_{94} = -83.6285454477006$$
$$x_{95} = 50.1418225850077$$