Proof of the law of cosines | Trig identities and examples | Trigonometry | Khan Academy 

ahhh that makes snese

@@teemo8247 thanks waited 12 years for someone to acknowledge it too

Your comment would apply much more to something like the Bretschneider's quadrilateral area formula being the so called complete version of Brahmagumpta's cyclic quadrilateral area formula because of the non-cyclic adaption term. However, in the case of the law of cosines as your last point states sure h^2=a^2+b^2-2ab*cos(pi/2) is in fact just h^2=a^2+b^2, but the important thing to bare in mind is that suppose you choose an angle t where the hypotenuse is adjacent annnnnd... side a arbitrarily, then b^2=a^2+h^2-2ah*cos(t) which isn't so arbitrary, and yet still applies to a right triangle. Yes, this isn't as simple as just saying b^2=h^2-a^2, and technically h*cos(t) is just a in trigonometric disguise so they are infact easy to show as equivalent, but that's not my point. My point really is that the pythagorean theorem isn't just some formula, nor is the law of cosines it's complete form or anything of that sort- I just find that logic completely disregards the pythagorean theorem as it's own entity and identity which is in my mind not alright. Now... if you re-phrase and say that the pythagorean theorem is a special case, even an identity, of the law of cosines for when you are finding the hypotenuse of a right triangle I'd say sure. The pythagorean theorem is in no way incomplete, as it never was intended to apply to any triangle except the very, VERY special family of right triangles. If this wasn't too tedious, I hope you found this helpful. I... don't mean to be harsh I just don't like it when things as fantastic as the pythagorean theorem get thrown out with the rest of the whole world of formulae... and the LAW of cosines for that matter. If you can't tell, I'm also one of the sticklers that says NEVER forget +c when you are doing an anti-derivative, and NO, an integral sign without bounds is NOT a sign saying "integrate the expression" it says to anti-differentiate the expression... and now I'm rambling, ranting, and raving. I hope there was something in here you found useful... if it wasn't too tedious or offensive. I mention Brahmagumpta and Bretschneider's area formulae because they are shown in Mathologer's most recent video on 1+2+3=1*2*3, the 3,4,5 triangle, and Heron's formula which is some awesome stuff I recommend you take a gander of. Good day!

@@rockysmith6105 why did you write so much to a youtub comment

That's so cool, I never realised. Thanks to you my Trig knowledge has broadened. You're 13 yr old comment helped me prepare for my upcoming Entrance exam, I hope you know that 🙏

I agree I get so ma like OMG WHY DO I FO THAT STOP JT

@@iliekmathphysics what?

Andre Duval you are an absolute maldad my friend.

Wow And I am just 14

@@PranabMallick. same homie (I never sleep cuz sleep is the cousin of death)

@@hanniballecter3727 ;-;

bro what

That's the power AND beauty of math IMO.

@@eduardoandrescontrerasrome6703 Yes, yes it sure is👍

*Tangents have left the chat*

no...you are welcome here

POV: The commentator was 40 when he wrote this comment. As of today in 2021, he is 47.

@@smackdashitoutchu7755 😂 yeah, but totally remember this vid...😎😉

Max Webster Uploaded on 2007, what did you expect?

+DOGE™ I expect an update.

badymojoy Valid point, but Khan has many other new topics to teach than reteaching trigonometry. Although you could ask him for an updated version, but the fact that no one is complaining means that Khan is okay not reteaching it.

+DOGE™ From what I've noticed, there are a small portion of videos on KA still using this low resolution, where things like equal signs look like c's. However small the minority, I consider myself part of those desiring to see an update of those videos--whenever Khan or someone else at KA's time permits.

still waiting

***** Quadratics.

Where does the 2cbcosØ come from?

When you expand any square like this (a-b)^2 it becomes (a-b)x(a-b) which you then use FOIL or any other method to multiply it out such that it gives you this: a*a - a*b + b*b - b*a. Which simplifies to: a^2 +b^2 -2ab.

I understand that, but how does this relate to my question? This occurs at 6:17 btw.

a^2 =

+Carl Silverstein I'm 57 too and still using it.

?

+Dman82499.....I use it in my job as a pipefitter to calculate angles and lengths of "travel" when they're not the standard 45 degrees.

There are thousands of proofs fro the pythagorean theorem that you can use and then use it to prove this so it is in no way circular

For*

+Charles Rambo Then cos theta would be negative, but there won't be problems.

Dru Dru if you could not follow what he was saying, you clearly are not use to trig and (a+b)^2

Buddy, links arent there

@@anindaaninda3383 RU-vid prevents me from posting the direct links. You have to copy the links and replace the similar part that is already in the present URL

LOL ur gunna be using this for the next couple of years bud, guarantee you see it again. You still have ways to go.

Lord Jean-Pierre haha its hard stuff

HarmlessGirlscout Lol I a m doing this in 7 grade

***** No, I lived in Texas.

teenroses Sorry, but this is the funnies thing I've read all day XD

😂😂😂

he means a year or two after highschool, when ur in college. but u learn trigonometry four years BEFORE college.