The coolest fact in trigonometry that you learn way too late

[Femme_physics]

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?

 

[statdad]

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

$$c^2 = a^2 + b^2 - 2ab$$

which is not the Pythagorean Theorem.

 

[Femme_physics]

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

Sorry

 

[least_action]

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?

yep it's awesome

 

[Hurkyl]

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

$$c^2 = a^2 + b^2 - 2ab$$

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).

 

[statdad]

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

Sorry

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.

 

[Mark44]

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.

 

[granpa]

http://thinkzone.wlonk.com/MathGems/MathGems.htm
[URL]http://thinkzone.wlonk.com/MathGems/pics/pythagorean_theorem.gif[/URL]

 

[Femme_physics]

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