Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$2 - 2 \cos{\left(x - 1 \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 1$$
$$x_{2} = 1 + 2 \pi$$
Numerical solution$$x_{1} = -36.6991114896456$$
$$x_{2} = 38.6991123485095$$
$$x_{3} = 19.8495560331216$$
$$x_{4} = -80.6814094421164$$
$$x_{5} = -5.28318554617199$$
$$x_{6} = -17.8495557968376$$
$$x_{7} = 101.530964423296$$
$$x_{8} = 88.964593962401$$
$$x_{9} = 95.2477791775533$$
$$x_{10} = -30.4159270346054$$
$$x_{11} = 13.5663695105623$$
$$x_{12} = 13.5663701178499$$
$$x_{13} = 19.8495554159042$$
$$x_{14} = -42.9822975075327$$
$$x_{15} = 63.8318531931265$$
$$x_{16} = 7.28318566694506$$
$$x_{17} = 82.6814095007727$$
$$x_{18} = 32.4159264380897$$
$$x_{19} = 82.6814100849983$$
$$x_{20} = 57.5486680202546$$
$$x_{21} = 13.5663708623807$$
$$x_{22} = -55.5486678808888$$
$$x_{23} = -17.8495554769708$$
$$x_{24} = 70.115038805167$$
$$x_{25} = 82.6814087697046$$
$$x_{26} = 7.28318486747256$$
$$x_{27} = -24.1327417326819$$
$$x_{28} = -93.2477791093241$$
$$x_{29} = 51.2654820224528$$
$$x_{30} = 1.00000044735768$$
$$x_{31} = 38.6991116117304$$
$$x_{32} = -24.1327411271999$$
$$x_{33} = -86.9645946639967$$
$$x_{34} = -74.3982234536233$$
$$x_{35} = -74.3982241868753$$
$$x_{36} = -86.9645938625694$$
$$x_{37} = 57.5486672704854$$
$$x_{38} = -68.1150382879088$$
$$x_{39} = -24.1327410652463$$
$$x_{40} = 26.1327414173968$$
$$x_{41} = -55.5486672497774$$
$$x_{42} = -49.2654827040023$$
$$x_{43} = 32.4159270482023$$
$$x_{44} = 76.3982235519432$$
$$x_{45} = 70.1150379433459$$
$$x_{46} = -93.2477787150689$$
$$x_{47} = -17.849556337754$$
$$x_{48} = -93.2477798617602$$
$$x_{49} = -80.681408426653$$
$$x_{50} = -11.5663706722839$$
$$x_{51} = 70.1150387480058$$
$$x_{52} = -61.8318534770036$$
$$x_{53} = -5.28318480393057$$
$$x_{54} = 95.2477799798464$$
$$x_{55} = -11.5663707217028$$
$$x_{56} = -36.6991122873847$$
$$x_{57} = 26.1327416644778$$
$$x_{58} = 26.132740802384$$
$$x_{59} = -30.4159262955782$$
$$x_{60} = 51.2654828234429$$
$$x_{61} = -80.6814086463278$$
$$x_{62} = -61.8318529849279$$
$$x_{63} = 76.3982241967455$$
$$x_{64} = 76.3982235970974$$
$$x_{65} = -30.4159275239453$$
$$x_{66} = 19.8495560513666$$
$$x_{67} = 63.8318525648093$$
$$x_{68} = -68.1150388809337$$
$$x_{69} = -99.5309643991898$$
$$x_{70} = 44.9822976021389$$
$$x_{71} = 44.9822968056677$$
$$x_{72} = -991.74327913164$$
$$x_{73} = 0.999999649022634$$
$$x_{74} = 88.9645947567955$$
$$x_{75} = -11.5663701006429$$
$$x_{76} = -42.9822967075459$$
$$x_{77} = -55.5486677788$$
$$x_{78} = -99.5309650399519$$
$$x_{79} = -61.8318526191255$$
$$x_{80} = 32.4159264376201$$
$$x_{81} = -74.3982245556249$$
$$x_{82} = -49.2654819565432$$
$$x_{83} = 63.8318531648007$$
$$x_{84} = -68.1150381847295$$