Components of a force. When do I use cos or sin?

[Vinny_S]

Here is an example of a problem I am having trouble with. I need to find the i, j, k of A. I have no issues with finding the components for B, but A I just can't wrap my head around when to use cos or sin. Especially here with double projection.

I know that A is :
(-10 cos70 sin30, 10 cos70 cos30, 10 sin70)

Any kind of an explanation regarding why I would do cos vs sin and vice versa would be greatly appreciated. I feel like I am missing something really obvious with this. Thank you.

 

[LCKurtz]

Since you are new here you may not be aware that bold facing is frowned on.

<Mark44: fixed>

Here is an example of a problem I am having trouble with. I need to find the i, j, k of A. I have no issues with finding the components for B, but A I just can't wrap my head around when to use cos or sin. Especially here with double projection.

I know that A is :
(-10 cos70 sin30, 10 cos70 cos30, 10 sin70)

When you say you "know" that do you mean you understand it or that that is what the answer book says?
If you use standard polar coordinates in the xy plane, the angle you have as 30 degrees would be labelled as $120^\circ$ from the x axis. The shadow of the 10 foot length on the xy plane would be $10\cos70$, so the x coordinate of A would be $10\cos(70)\cos(120)$. But $\cos 120 = -\sin 30$, so that is where your x coordinate comes from. Can you take it from there?