As J.M.'s been saying, the lengths of the horizonatal and vertical sides of the right handed triangle will be given by cos(a) and sin(a) respectively (where a is the angle between 0 and 360 degrees.)
This comes straight from the geometric definitions of cosine and sine: cos(a) is often defined as 'adjacent divided by hypotenuse.' However, as your hypotenuse is just 1, then the cos(a) = (the length of the adjacent side) = the length of the side on the x axis.
Similarly, sin(a) = the length of the opposite side = the length of the side on the Y axis.
Hope that makes some sense. You'll find that the negatives and positives are all accounted for as you swing around the circle. Look at http://en.wikipedia.org/wiki/Unit_circle
if you want an overload of info :D