ITYM sin not cos; the former intersects y=x for integers, while the later intersects for multiples of 0.5. And the extremums would be at n + (-1)ⁿ sin^-1( 1 / rπ )/π (for integer n).

</pedant> :)

Update: Gah, I had 2π rather than rπ because I used that as the constant when I checked things.