Why does quadrant 2 come before quadrant 1?

Answer 1

It doesn't. Its a matter of interpretation.

When drawing the unit circle, we start at x=1, y=0. As we draw, maintaining a radius of 1 from the origin at x=0, y=0, we proceed counter-clockwise. Initially, both x and y are positive. That is quadrant 1. When x becomes negative at x=0, y=1, that is quadrant 2. When y becomes negative at x=-1, y=0, that is quadrant 3. And when x becomes positive again at x=0, y=-1, that is quadrant 4.

So you see, its all in the perspective of which comes first, and in trigonometry, the vector where theta = 0 comes first, not where your eye just happens to scan from left to right.