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

Femme_physics

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 gonna 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 theorm!!! 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

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

which is not the Pythagorean Theorem.

Femme_physics

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

Sorry

least_action

yep it's awesome

Hurkyl

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

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

You don't need the law of cosines to conclude 0 = 0.

granpa

http://thinkzone.wlonk.com/MathGems/MathGems.htm

Femme_physics

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