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

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In summary, the conversation is about someone trying to understand the proof of breaking up an acute and obtuse triangle and solving it using trigonometry and Pythagoras. They have some confusion about a specific part involving the -2bc cos formula and are wondering if they are on the right track by looking at the proof via a unit circle. They mention that their books do not show this proof and they are preparing for exams where they only need to remember the formulae. They ask for more specific help in understanding the proof and plan to post a diagram and explanation the next day.
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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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  • #2
Try to be more specific. You might list the steps of the proof and show where you have a problem.
 
  • #3
Sorry for being vague, been stuck on this all day. I will post a diagram tomorrow and try and explain how I see it.
 

What is the cosine rule?

The cosine rule, also known as the law of cosines, is a formula used to find the length of a side or measure of an angle in a non-right triangle. It states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.

What is the sine rule?

The sine rule, also known as the law of sines, is a formula used to find the length of a side or measure of an angle in a triangle. It states that the ratio of the length of a side to the sine of the angle opposite that side is equal to the same ratio for the other two sides and angles in the triangle.

When should I use the cosine rule?

The cosine rule is used when you know the lengths of two sides and the measure of the included angle in a non-right triangle, and need to find the length of the third side or measure of an angle. It is also used to solve problems involving oblique triangles, which have no right angles.

When should I use the sine rule?

The sine rule is used when you know the length of one side and the measure of two angles in a triangle, and need to find the length of another side or measure of an angle. It can also be used to solve problems involving triangles with one right angle.

What is the difference between the cosine rule and the sine rule?

The main difference between the cosine rule and the sine rule is that the cosine rule is used for non-right triangles, while the sine rule can be used for both right and non-right triangles. Additionally, the cosine rule involves the cosine function, while the sine rule involves the sine function.

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