Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(6 x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{6}$$
Numerical solution$$x_{1} = 82.2050077689329$$
$$x_{2} = 62.3082542961976$$
$$x_{3} = 97.9129710368819$$
$$x_{4} = -41.8879020478639$$
$$x_{5} = 14.1371669411541$$
$$x_{6} = -68.0678408277789$$
$$x_{7} = 72.2566310325652$$
$$x_{8} = -43.9822971502571$$
$$x_{9} = -90.0589894029074$$
$$x_{10} = 9.94837673636768$$
$$x_{11} = 12.0427718387609$$
$$x_{12} = -37.6991118430775$$
$$x_{13} = 34.5575191894877$$
$$x_{14} = -49.7418836818384$$
$$x_{15} = -75.9218224617533$$
$$x_{16} = -51.8362787842316$$
$$x_{17} = -21.9911485751286$$
$$x_{18} = 50.2654824574367$$
$$x_{19} = -15.707963267949$$
$$x_{20} = -46.0766922526503$$
$$x_{21} = -2.0943951023932$$
$$x_{22} = 67.5442420521806$$
$$x_{23} = 21.9911485751286$$
$$x_{24} = -87.9645943005142$$
$$x_{25} = -90.5825881785057$$
$$x_{26} = 70.162235930172$$
$$x_{27} = 4.18879020478639$$
$$x_{28} = 38.2227106186758$$
$$x_{29} = 34.0339204138894$$
$$x_{30} = -31.9395253114962$$
$$x_{31} = 60.2138591938044$$
$$x_{32} = -59.1666616426078$$
$$x_{33} = -85.870199198121$$
$$x_{34} = -29.845130209103$$
$$x_{35} = -78.0162175641465$$
$$x_{36} = -384.84510006475$$
$$x_{37} = 48.1710873550435$$
$$x_{38} = -17.8023583703422$$
$$x_{39} = 10.471975511966$$
$$x_{40} = -93.7241808320955$$
$$x_{41} = -65.9734457253857$$
$$x_{42} = 46.0766922526503$$
$$x_{43} = -83.7758040957278$$
$$x_{44} = 28.2743338823081$$
$$x_{45} = 94.2477796076938$$
$$x_{46} = 75.9218224617533$$
$$x_{47} = 96.342174710087$$
$$x_{48} = -82.2050077689329$$
$$x_{49} = 6.28318530717959$$
$$x_{50} = -25.6563400043166$$
$$x_{51} = 93.2005820564972$$
$$x_{52} = 36.1283155162826$$
$$x_{53} = -19.8967534727354$$
$$x_{54} = -12.0427718387609$$
$$x_{55} = 80.1106126665397$$
$$x_{56} = -61.7846555205993$$
$$x_{57} = 56.025068989018$$
$$x_{58} = -24.0855436775217$$
$$x_{59} = -56.025068989018$$
$$x_{60} = 78.0162175641465$$
$$x_{61} = 0$$
$$x_{62} = 18.3259571459405$$
$$x_{63} = 58.1194640914112$$
$$x_{64} = -39.7935069454707$$
$$x_{65} = -9.94837673636768$$
$$x_{66} = 2.0943951023932$$
$$x_{67} = -34.0339204138894$$
$$x_{68} = -100.007366139275$$
$$x_{69} = -95.8185759344887$$
$$x_{70} = 24.0855436775217$$
$$x_{71} = 99.4837673636768$$
$$x_{72} = 40.317105721069$$
$$x_{73} = -97.9129710368819$$
$$x_{74} = 100.007366139275$$
$$x_{75} = -53.9306738866248$$
$$x_{76} = 31.9395253114962$$
$$x_{77} = -3.66519142918809$$
$$x_{78} = 92.1533845053006$$
$$x_{79} = 87.9645943005142$$
$$x_{80} = 84.2994028713261$$
$$x_{81} = 53.9306738866248$$
$$x_{82} = 43.9822971502571$$
$$x_{83} = -81.6814089933346$$
$$x_{84} = -63.8790506229925$$
$$x_{85} = -73.8274273593601$$
$$x_{86} = 68.0678408277789$$
$$x_{87} = 26.1799387799149$$
$$x_{88} = 16.2315620435473$$
$$x_{89} = -71.733032256967$$
$$x_{90} = -59.6902604182061$$
$$x_{91} = 65.9734457253857$$
$$x_{92} = 90.0589894029074$$
$$x_{93} = -7.85398163397448$$
$$x_{94} = -5.75958653158129$$
$$x_{95} = -27.7507351067098$$