Find a translation that fixes the graph of cosine function

Find a translation that fixes $y=\cos x$

That is, the goal is a translation of the plane that fixes this curve:

I have tried this numerous times but can't seem to find a method of doing it. The article on translation says it has no fixed points, which confuses me. How can it fix the curve, if it does not fix any point?

• Translation does not fix any point of the real line, but it still can fix values of cosine. Think about how cosine repeats. – Adam Saltz Feb 8 '13 at 12:41
• The translation by a nonzero $x$ increment can fix the curve $y=\cos(x)$ without fixing any single point. That is, the translation of the curve is the same curve; the translation of each point is a different point. – hardmath Feb 8 '13 at 12:43
• I do not understand the close votes here. The question is not unclear, and the link is no issue because the OP summarizes their issue with it. – user1729 Aug 6 '14 at 8:41

Move it by $2\pi$ to the right.
$$\cos(x-2\pi)=\cos(x)$$