Alright, so I've always had trouble with this and I finally decided to try and get a real answer that I can retain.

I've got 2 pictures here and here

On both diagrams you can see the picture I'm given and my little pencil tool drawn in additions. The cos/sin and positive/negative signs should be right considering I took them from the solutions manual.

I can get the cos and sin parts, but how do they get the negative or positive signs. I thought I found a pattern in the second one, but when I applied the same rules to the first one it didn't work.

I'm just trying to get the i and j vector components to multiply my F magnitude portion to. So like on the triangle one it would be

F^1on3 = 1.7936*10^-4 (cos(60)i sin(60)j)

and

f^2on3 = 1.7936*10^-4 (-cos(60)i sin(60)j)

but i don't know why the second cos is negative.

pls help math gods.