El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\sin{\left(\sqrt{13} x \right)} + \cos{\left(\sqrt{13} x \right)} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \frac{\sqrt{13} \pi}{52}$$
Solución numérica$$x_{1} = -85.6072912665696$$
$$x_{2} = 11.9806641721662$$
$$x_{3} = -97.8057856964116$$
$$x_{4} = -43.7838817928257$$
$$x_{5} = -69.9235127139156$$
$$x_{6} = 64.2599260143461$$
$$x_{7} = -62.0816234375886$$
$$x_{8} = 36.3776530318502$$
$$x_{9} = 25.9218006634142$$
$$x_{10} = 42.4769002467712$$
$$x_{11} = -28.1001032401717$$
$$x_{12} = 44.2195423081772$$
$$x_{13} = 38.1202950932562$$
$$x_{14} = 68.6165311678611$$
$$x_{15} = -68.1808706525096$$
$$x_{16} = 45.9621843695832$$
$$x_{17} = 93.8848410582481$$
$$x_{18} = 24.1791586020082$$
$$x_{19} = -11.5450036568147$$
$$x_{20} = 72.1018152906731$$
$$x_{21} = 52.0614315845041$$
$$x_{22} = -48.1404869463407$$
$$x_{23} = -76.0227599288366$$
$$x_{24} = 59.0319998301281$$
$$x_{25} = -75.1514388981336$$
$$x_{26} = -99.5484277578175$$
$$x_{27} = 22.4365165406022$$
$$x_{28} = -55.9823762226676$$
$$x_{29} = -34.1993504550927$$
$$x_{30} = -45.5265238542317$$
$$x_{31} = 87.7855938433271$$
$$x_{32} = -35.9419925164987$$
$$x_{33} = -42.9125607621227$$
$$x_{34} = 84.3003097205151$$
$$x_{35} = -63.8242654989946$$
$$x_{36} = -19.3868929331417$$
$$x_{37} = -14.1589667489237$$
$$x_{38} = 78.2010625055941$$
$$x_{39} = -89.9638964200846$$
$$x_{40} = 66.8738891064551$$
$$x_{41} = -37.6846345779047$$
$$x_{42} = 10.2380221107602$$
$$x_{43} = 98.2414462117631$$
$$x_{44} = -17.6442508717357$$
$$x_{45} = 73.8444573520791$$
$$x_{46} = 66.0025680757521$$
$$x_{47} = 32.0210478783352$$
$$x_{48} = -15.9016088103297$$
$$x_{49} = -9.80236159540873$$
$$x_{50} = -51.6257710691526$$
$$x_{51} = -57.7250182840736$$
$$x_{52} = 97.3701251810601$$
$$x_{53} = -8.05971953400273$$
$$x_{54} = 53.8040736459101$$
$$x_{55} = 56.4180367380191$$
$$x_{56} = 5.88141695724524$$
$$x_{57} = 99.984088273169$$
$$x_{58} = 50.3187895230982$$
$$x_{59} = -65.5669075604006$$
$$x_{60} = 70.3591732292671$$
$$x_{61} = -82.1220071437576$$
$$x_{62} = 2.39613283443325$$
$$x_{63} = 92.1421989968421$$
$$x_{64} = 79.9437045670001$$
$$x_{65} = 18.0799113870872$$
$$x_{66} = -71.6661547753216$$
$$x_{67} = -23.7434980866567$$
$$x_{68} = -83.8646492051636$$
$$x_{69} = -54.2397341612616$$
$$x_{70} = 4.13877489583924$$
$$x_{71} = 39.8629371546622$$
$$x_{72} = -58.5963393147766$$
$$x_{73} = -29.8427453015777$$
$$x_{74} = -31.5853873629837$$
$$x_{75} = -88.2212543586786$$
$$x_{76} = 59.9033208608311$$
$$x_{77} = 9.36670108005723$$
$$x_{78} = 101.726730334575$$
$$x_{79} = -3.70311438048774$$
$$x_{80} = 58.1606787994251$$
$$x_{81} = 90.3995569354361$$
$$x_{82} = -91.7065384814906$$
$$x_{83} = -0.21783025767575$$
$$x_{84} = 76.4584204441881$$
$$x_{85} = -49.8831290077467$$
$$x_{86} = -22.0008560252507$$
$$x_{87} = -96.0631436350056$$
$$x_{88} = 30.2784058169292$$
$$x_{89} = 86.0429517819211$$
$$x_{90} = 33.7636899397412$$
$$x_{91} = 40.7342581853652$$
$$x_{92} = 16.3372693256812$$
$$x_{93} = -77.7654019902426$$
$$x_{94} = -1.96047231908175$$
$$x_{95} = 19.8225534484932$$
$$x_{96} = -42.0412397314197$$