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

1. Sep 24, 2010

### 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 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???

2. Sep 24, 2010

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

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.

3. Sep 24, 2010

### Femme_physics

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

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

Sorry

4. Sep 24, 2010

### least_action

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

yep it's awesome

5. Sep 24, 2010

### Hurkyl

Staff Emeritus
Re: The coolest fact in trigonometry that you learn way too late....

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).

6. Sep 24, 2010

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

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.

7. Sep 24, 2010

### Staff: Mentor

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

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

8. Sep 24, 2010

### granpa

Last edited by a moderator: Apr 25, 2017
9. Sep 25, 2010

### Femme_physics

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

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