I know sum[k=1,n] k = [n(n+1)]/2, but what about Σ cos(k) =?

[kapax]

Hi, all!

Recently I calculated some summations, such as:

. . . . .$\displaystyle \displaystyle \sum_{k=1}^n\, k\, =\, \dfrac{n\,(n\, +\, 1)}{2}$

The idea of the summation of cos(k) just popped up in my head:

. . . . .$\displaystyle \displaystyle \sum_{k=1}^n\, \cos(k)\, =\, ?$

I have googled a lot, but none of the results seems to be about this kind of question.