[VECTORS] Rotation without trigonometry

How is it done?
Normally, rotating a vector A(x1, y1) through t radians in order to get vector B(x2, y2) is done with
x2 = x1*cos(t) - y1*sin(t),
y2 = x1*sin(t) + y1*cos(t).

But trigonometry is expensive, especially without an FPU, so there must be another way.
I was thinking of something similar to Bresenham's circle algorithm, or perhaps reflecting the vector about the origin or something.

So, uh, how would you do it?

If you don't have an FPU, and you're going to end up on lattice points, you may want to look into continued fractions, which rely pretty much exclusively on integers.