I would start by showing that you can get arbitrarily point to any point iff you can make arbitrarily small points on the x- and y-axes. I would then try to find what scenarios let you construct these arbitrarily small points on the x- and y-axes. It should relate to particular ratios of trig functions being irrational, which we expect to happen most of the time. But certainly not all of it! You have an advantage setting this up for the x-axis because you get the vector (1, 0) for free; the y-axis is a little more difficult, for Reasons.