Cosine Rule , what good is it ?

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    Cosine Cosine rule
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Discussion Overview

The discussion revolves around the application and validity of the Cosine Rule in scenarios involving negative lengths, particularly in vector contexts such as displacement and velocity. Participants explore whether negative values can be incorporated into the formula and how to interpret these values in geometric problems.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the validity of the Cosine Rule when using negative lengths, citing a specific problem involving -15 km and 10 km with a 60-degree angle.
  • Another participant asserts that negative lengths do not exist, suggesting that negative values can refer to coordinates rather than actual lengths.
  • A participant introduces the idea that the angle could be considered negative if interpreted in a directional context, such as east of north.
  • There is a discussion about whether negative displacement is applicable to the Cosine Rule.
  • One participant emphasizes that while vector components can be negative, the lengths themselves should always be treated as non-negative when applying the Cosine Rule.
  • A question is raised about whether to use the magnitude of a velocity (e.g., -15 km/hr) as a side length in a triangle, to which another participant confirms that only the magnitude should be used.

Areas of Agreement / Disagreement

Participants generally disagree on the treatment of negative lengths in the context of the Cosine Rule, with some asserting that negative lengths are not valid while others explore the implications of negative values in vector quantities.

Contextual Notes

The discussion highlights the distinction between vector components and actual lengths, as well as the importance of magnitude in geometric applications. There is an unresolved tension regarding the interpretation of negative values in relation to the Cosine Rule.

Who May Find This Useful

This discussion may be of interest to students and practitioners in physics and mathematics who are exploring vector quantities, geometric principles, and the application of the Cosine Rule in various contexts.

junior_J
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Cosine Rule , what good is it ?

Does the Cosine rule hold true for say negative lengths ? as in a vector quantity like displacement ?

I came across this problem which had -15km and 10km as the known sides whereas the angle opposite the unkown side is 60 degree ...

I tries using c^2 = a^2 + b^2 - 2*a*b cosC but this didnt work ... then on account of frustration i forcibly changed the '-' part of the formula to a '+' only to find that it works ... ?

Can someone explain this to me ??
 
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ther is no such thing as negative lenght, there is negative coordinates since somepoint has to be 0 and one side will be posetive and the other negative
 
the 60 degrees is negative, because it is east of north.
 
negative displacement ? would that apply to the cosine rule ?
 
There is no such thing as a negative length. A vector quantity (say, in a one-dimensional problem on a number line), or the components of the vector might be negative but the length is always non-negative. If you are using the cosine law in a vector problem, use the lengths, not the components.
 
so if i had a velocity oh say -15 km/hr ... id use 15 instead of -15 ?? as one of the sides of a triangle ?
 
yes you would, because you only care about magnitude. The direction comes later.
 

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