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

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

cosine

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?

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    $\begingroup$ Translation does not fix any point of the real line, but it still can fix values of cosine. Think about how cosine repeats. $\endgroup$ – Adam Saltz Feb 8 '13 at 12:41
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    $\begingroup$ 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. $\endgroup$ – hardmath Feb 8 '13 at 12:43
  • $\begingroup$ 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. $\endgroup$ – user1729 Aug 6 '14 at 8:41
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Move it by $2\pi$ to the right.

Yes, the translation itself (unless by zero vector) has no fixed points. It is about the graph of your function, it won't have fixed point either under the translation, but the translated points together will give exactly the same graph.

$$\cos(x-2\pi)=\cos(x)$$

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