mini challenge: find the smallest cosine of an integer

[EdS2]

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Naturally, we should use radians for this, and we're interested in the absolute value of the cosine. Some calculators will have a maximum integer that they are happy to take the cosine of, which will of course affect your result. But there are no prizes, so start your search - whether manually, programatically, or mathematically. Show your working!

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cos(0) is the first, and the worst...
cos(1) is better, and could hardly be otherwise...
cos(2) is better yet
cos(5) is a new record
cos(8) is another winner
cos(11) is pretty good! (And surely no coincidence)