Why do we inverse figures in their absence for vectors?

Question

Two people push horizontally on a box, exerting the forces shown:

$F_1$ :

$x$ component $6 \sin 40^{\circ} = 3.86$

$y$ component $-6 \cos 40^{\circ} = -4.60$

$F_2$ :

$x$ component $-5 \sin 30^{\circ} = -2.50$

$y$ component $5 \cos 30^{\circ} = 4.33$

Two questions please:

1: Why do we inverse the newtons?

2: Why is $F_1$, going south east keeping the $6$ newtons as its $x$ component, but $F_2$, going north east using it's $5$ newtons as its $y$ component? example, Why are they NOT BOTH in the $x$ or the $y$?

Answer 1

1. We don't. Negative is left/down, positive is right/up. Thus, the vector going up and left has positive $y$ component and negative $x$ component, and the vector going down and right has positive $x$ component and negative $y$ component.
2. I have no idea what you mean: both have both an $x$ and a $y$ component, and while their respective magnitudes are used to compute both, neither is equal to the magnitude.