Understanding the Proof of Cosine and Sine Rules: Am I on the Right Track?

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SUMMARY

The discussion centers on the understanding and proof of the Cosine and Sine Rules, particularly in relation to acute and obtuse triangles. The user is exploring the proof using the unit circle, specifically focusing on the negative x quadrant, and is seeking confirmation on their approach. They reference the cosine formula, particularly the -2bc cos component, and express confusion about this aspect. The user aims to solidify their understanding of the proofs rather than merely memorizing the formulas.

PREREQUISITES
  • Understanding of basic trigonometry concepts
  • Familiarity with the unit circle and its quadrants
  • Knowledge of the Pythagorean theorem
  • Ability to work with the Cosine Rule and Sine Rule
NEXT STEPS
  • Study the derivation of the Cosine Rule using the unit circle
  • Review the properties of triangles in different quadrants of the unit circle
  • Practice solving problems involving obtuse triangles using the Cosine Rule
  • Examine visual proofs of the Sine and Cosine Rules for better conceptual understanding
USEFUL FOR

Students of mathematics, particularly those studying trigonometry and geometry, as well as educators seeking to clarify the proofs of the Sine and Cosine Rules.

Taylor_1989
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At the moment I a trying to really get to grips with these rules proof wise. I would like to know if I am on the right track in learning the proof correctly. In my books it goes through the proof in breaking up an acute and obtuse triangle and the solving via trigonometry/Pythagoras.

I understand all right until the part on an obtuse triangle until it gets to the - 2bc cos part, I took that from the c2 formulae of cosine. I don't really want anyone telling me why it like this more, am I going in the right direction, by looking a the proof via a unit circle, and looking in the negative x quadrant? My books do not show this proof nor do they show the unit circle, as like most per degree exams, I don't need to show the proof just remember the formulae and apply the correctly.

So am I heading in the right direction in understanding the proof?
 
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Try to be more specific. You might list the steps of the proof and show where you have a problem.
 
Sorry for being vague, been stuck on this all day. I will post a diagram tomorrow and try and explain how I see it.
 

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