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Mechanics- Resolving Forces(When to apply sin/cos)?

I understand that with a force F, we can multiply the magnitude of F with sin/cos of the angle between the force and the direction of motion to find the component of the force. What my textbook does NOT explain at all is when to use sin to resolve forces, and when to use cos.

I need an explanation that is sufficient such that I can always use the right trigonometric function. Could anyone help, please? :smile:
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(edited 5 years ago)
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Illidan2
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In the diagram provided, I see exactly how that works. But suppose I had an angle that was adjacent to the vertical component, and opposite the horizontal component- would it be the other way around? Would I then use cos to resolve vertically, and sine for horizontal?

Or is the vertical component relative to the angle rather than absolute, and thus would never be adjacent to the angle?
Original post by psc---maths
Postey removey
(edited 5 years ago)
Original post by Illidan2
In the diagram provided, I see exactly how that works. But suppose I had an angle that was adjacent to the vertical component, and opposite the horizontal component- would it be the other way around? Would I then use cos to resolve vertically, and sine for horizontal?

Or is the vertical component relative to the angle rather than absolute, and thus would never be adjacent to the angle?


1) You can exploit the known shape of the sine and cosine curves. If the known angle @ is acute (which it very often is), consider how the turning effect of the force would change if @ were to be increased or decreased. If the turning effect of the force would tend to increase with increasing @, were talking sin. Otherwise it's cos. Similarly, you can consider what would happen to the turning effect of the force if @ was zero or 90deg, then apply similar reasoning.

2) Remember that, in the end, the moment of a force F about point A is the perpendicular distance from A to F. Although it may take a little longer you can always draw the triangle that includes this perpendicular, and once you've done that it should be clear whether a particular side of the triangle in opposite or adjacent to @.

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