The coolest fact in trigonometry that you learn way too late

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Discussion Overview

The discussion revolves around a participant's realization regarding the law of cosines and its relationship to the Pythagorean theorem, particularly in the context of right triangles. The conversation explores the implications of this relationship and the understanding of trigonometric concepts.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses excitement about discovering that the law of cosines for a right triangle can be seen as the Pythagorean theorem, stating that when angle A is zero, it simplifies to c² = a² + b² - 2abCosA.
  • Another participant challenges this interpretation, noting that if A = 0, then cos A = 1, leading to the equation c² = a² + b² - 2ab, which does not represent the Pythagorean theorem.
  • A different participant suggests that A is actually 90 degrees, implying a misunderstanding of the angle's value in the context of the law of cosines.
  • One participant emphasizes that the conclusion of 0 = 0 does not require the law of cosines, suggesting that the relationship is more straightforward than initially presented.
  • Another participant shares links to external resources related to the Pythagorean theorem, indicating interest in further exploration of the topic.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the law of cosines and its connection to the Pythagorean theorem. There is no consensus on the correctness of the initial claim, and the discussion remains unresolved regarding the implications of the angle A.

Contextual Notes

The discussion includes assumptions about the values of angles in the context of the law of cosines and the Pythagorean theorem, which may not be fully articulated by all participants. There are also unresolved mathematical interpretations regarding the simplifications presented.

Femme_physics
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The coolest fact in trigonometry that you learn way too late...

So I just spent the last 12 hours learning trig (occasional food breaks).

I just want to share with you something really, really, really, really, awesome.


Check this out, you're going to be blown away

The law of cosines, applied to a right triangle is c^2 = a^2+b^2 - 2abCosA Whereas A is equal to zero!

So the law of cosines for a right triangle is, in fact, the Pythagorean theorem! Math is sooooooooo awesome. Why did it only take me the last quarter of the textbook to learn this fact?
 
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Perhaps I'm missing something here, but if A = 0, cos A = 1, and your statement comes in as

[tex] c^2 = a^2 + b^2 - 2ab[/tex]

which is not the Pythagorean Theorem.
 


I mean, A is 90 degrees and therefor 0 is equal to 0!

Sorry :blushing:
 


Dory said:
Check this out, you're going to be blown away

The law of cosines, applied to a right triangle is c^2 = a^2+b^2 - 2abCosA Whereas A is equal to zero!

So the law of cosines for a right triangle is, in fact, the Pythagorean theorem! Math is sooooooooo awesome. Why did it only take me the last quarter of the textbook to learn this fact?

:biggrin:

yep it's awesome
 


statdad said:
Perhaps I'm missing something here, but if A = 0, cos A = 1, and your statement comes in as

[tex] c^2 = a^2 + b^2 - 2ab[/tex]

which is not the Pythagorean Theorem.

Of course, this value is interesting too, as it's the theorem that if you have three collinear points:
A --- B ---- C​
Then the length of the whole (b) is the sum of the lengths of the two parts (a and c).
 


Dory said:
I mean, A is 90 degrees and therefor 0 is equal to 0!

Sorry :blushing:

Don't worry - I had a feeling this is what you meant - but I wanted to make sure.

You'll find lots of cool things in your math classes if you take the time to look around.
 


Dory said:
I mean, A is 90 degrees and therefor 0 is equal to 0!
You don't need the law of cosines to conclude 0 = 0.
 


Awesome link granpa! And thanks for the replies and humoring me :)
 

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