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

In summary, the conversation is about finding the i, j, k components of vector A and the difficulty in understanding when to use cos or sin in double projection. The coordinates of A are (-10 cos70 sin30, 10 cos70 cos30, 10 sin70). The explanation for using cos and sin in this scenario is provided using standard polar coordinates in the xy plane.
  • #1
Vinny_S
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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.

media%2Fed8%2Fed8d3315-6495-41e1-afcf-5b9dccfa364a%2FphpPuMTKo.png


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

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Vinny_S said:
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.

media%2Fed8%2Fed8d3315-6495-41e1-afcf-5b9dccfa364a%2FphpPuMTKo.png


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?
 

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

1. What are the components of a force?

The components of a force are the two perpendicular vectors that make up the force: the horizontal component and the vertical component.

2. How do I determine the horizontal and vertical components of a force?

The horizontal and vertical components can be determined using trigonometric functions, specifically cosine (cos) and sine (sin). Cosine is used to find the horizontal component, while sine is used to find the vertical component.

3. When do I use cosine (cos) to find the horizontal component?

Cosine is used to find the horizontal component when the angle between the force vector and the horizontal axis is known.

4. When do I use sine (sin) to find the vertical component?

Sine is used to find the vertical component when the angle between the force vector and the vertical axis is known.

5. Can I use both cosine (cos) and sine (sin) to find the components of a force?

Yes, both cosine and sine can be used to find the components of a force as long as the angles between the force vector and the horizontal/vertical axes are known.

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