We have been given a function [tex]y=\cos(x)[/tex]. We are asked to find the formula which gives the x-coordinates of the maximum values for given function.
We know that cosine function oscillates between [tex]-1[/tex] and 1 that is minimum value of cosine is [tex]-1[/tex] and maximum value is [tex]1[/tex].
We also know that [tex]\cos(0)=1[/tex] and after period of cosine is [tex]2\pi[/tex]. This means after every [tex]2\pi[/tex], we will get to [tex]1[/tex].
So maximum of cosine is [tex]2\pi n[/tex], where n is an integer.
Therefore, our required formula is [tex]2\pi n[/tex], where, [tex]n=0,\pm 1,\pm 2,\pm3,...[/tex]