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

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The discussion focuses on understanding the proofs of the cosine and sine rules, particularly in relation to acute and obtuse triangles. The user is grappling with the application of the cosine formula, especially the -2bc cos component in obtuse triangles. They are exploring the proof using a unit circle and the negative x quadrant, which is not covered in their textbooks. The user seeks confirmation on whether this approach is valid for grasping the proof, despite the exam requirements emphasizing formula memorization over proof demonstration. Overall, the user is looking for clarity on their understanding of the proof process.
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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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