Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\cos{\left(\frac{x}{3} - 5 \right)} - 1 = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 15$$
$$x_{2} = 15 + 6 \pi$$
Numerical solution$$x_{1} = -60.398225167194$$
$$x_{2} = 14.9999988261632$$
$$x_{3} = -41.5486692725727$$
$$x_{4} = 90.3982227224037$$
$$x_{5} = -79.2477781029098$$
$$x_{6} = 14.999998458996$$
$$x_{7} = -98.097334562244$$
$$x_{8} = 14.9999997146293$$
$$x_{9} = 52.6991116051083$$
$$x_{10} = -79.2477803321481$$
$$x_{11} = 71.5486662729243$$
$$x_{12} = -98.0973340232512$$
$$x_{13} = 90.398223596696$$
$$x_{14} = -3.84955738562815$$
$$x_{15} = 33.8495569083246$$
$$x_{16} = -79.2477782708537$$
$$x_{17} = 71.5486693049611$$
$$x_{18} = 52.6991107702266$$
$$x_{19} = 71.54866643115$$
$$x_{20} = -60.3982228243784$$
$$x_{21} = 90.3982251064929$$
$$x_{22} = -79.2477789841353$$
$$x_{23} = -41.5486663322582$$
$$x_{24} = -41.5486688314017$$
$$x_{25} = -22.6991114520374$$
$$x_{26} = 71.548668029236$$
$$x_{27} = -60.3982221493397$$
$$x_{28} = 90.3982251009654$$
$$x_{29} = 33.8495574342307$$
$$x_{30} = 71.54866948053$$
$$x_{31} = -60.3982226100855$$
$$x_{32} = 52.6991131935032$$
$$x_{33} = -3.84955504975715$$
$$x_{34} = -173.49556300409$$
$$x_{35} = -3.8495567900673$$
$$x_{36} = 33.8495551743668$$
$$x_{37} = -60.398224329258$$
$$x_{38} = 15.0000015363515$$
$$x_{39} = 90.3982200759343$$
$$x_{40} = -41.5486711953331$$
$$x_{41} = 52.6991133380664$$
$$x_{42} = 33.849559522518$$
$$x_{43} = -98.0973362982451$$
$$x_{44} = -98.0973354487839$$
$$x_{45} = -79.2477810482348$$
$$x_{46} = -79.2477798706684$$
$$x_{47} = -41.5486710728419$$
$$x_{48} = 52.6991124893956$$
$$x_{49} = 71.5486671442574$$
$$x_{50} = 52.699111045689$$
$$x_{51} = -22.6991133695471$$
$$x_{52} = -22.6991106660189$$
$$x_{53} = 52.6991103118927$$
$$x_{54} = 52.6991101149785$$
$$x_{55} = -41.5486678817393$$
$$x_{56} = 71.5486685591574$$
$$x_{57} = -22.6991131087023$$
$$x_{58} = -3.84955445341867$$
$$x_{59} = -41.5486687481687$$
$$x_{60} = 14.9999994759325$$
$$x_{61} = 33.849554516242$$
$$x_{62} = 14.9999996226036$$
$$x_{63} = -98.0973343764819$$
$$x_{64} = -60.3982250331757$$
$$x_{65} = -79.2477811421677$$
$$x_{66} = -60.3982234469601$$
$$x_{67} = -79.2477806989887$$
$$x_{68} = 33.8495560338965$$
$$x_{69} = 14.9999996057432$$
$$x_{70} = 90.3982225740357$$
$$x_{71} = -41.5486663557103$$
$$x_{72} = 33.8495570322901$$
$$x_{73} = 90.3982244584232$$
$$x_{74} = 90.3982221847585$$
$$x_{75} = -41.5486670141914$$
$$x_{76} = -3.84955720208902$$
$$x_{77} = 71.5486688591282$$
$$x_{78} = -3.84955461250715$$
$$x_{79} = 33.8495545081941$$
$$x_{80} = 15.0000012688973$$
$$x_{81} = -22.699111269591$$
$$x_{82} = -60.3982216595791$$
$$x_{83} = 15.0000015442757$$
$$x_{84} = -22.6991102947873$$
$$x_{85} = 15.0000005154463$$
$$x_{86} = -3.8495557964631$$
$$x_{87} = -22.6991123554547$$
$$x_{88} = -22.6991114630313$$