Law of Cosines - Formula, Examples & Proof - [2-20-4]

[@kate6370]

Sir, I became your subscriber last 2019! I'm so happy that you're still active here on KZbin. Thank you for sharing your knowledge to us!

[@sohampatel6122]

Hello Jason! You are a very great teacher. For me, trigonometry was very hard until watching your videos step by step which made me very proficient in the subject! I even started explaining your subjects to my family and they became proud! Keep up the great work, thank you.

[@MathAndScience]

You are very welcome!

[@ullastvtl]

Trigonometry was my dreaded Bugaboo during my teenage. Today at 61 years, I understand it without fear. Thank you very much, Mr. Polymath Jason.

[@donsena2013]

My preference is first to derive the law of cosines from the Pythagorean Theorem and to show the Pythagorean Theorem to be simply a special case of the law of cosines, as the included angle in the cross-product term approaches 90 degrees, thus zeroing out that last term. The law of cosines can be derived from a simple vector analysis, starting with the definition of the dot product, and independently of the Pythagorean Theorem.

[@irishamerican4558]

I doubt he cares what your preferences are.

[@donsena2013]

@@irishamerican4558 He should. Law of cosines by use of the dot product: kzbin.info/www/bejne/onLToWhtgNd4e6c

[@monak4854]

The gift that keeps on giving. Thank you 🙏

[@vascobishop3359]

Good teacher who pick some excellent points and topics. Has anyone seen his unit of circle lesson? Amazing content.

[@simpleman283]

Many times. So many times in fact that I noticed a pattern on it just the other day, that now I can even figure what the radian of any angle on the unit circle will be. You are correct, Amazing content, indeed.

[@ercussio]

This video was an adventure of mathematical understanding. Thank you!

[@nicholaswang-g6u]

This explanation was very simple to understand, thank you.

[@keabetswekwenda5760]

Thank you very much sir it was helpful I used to struggle a lot before I started watching your videos you are much appreciated

[@MathAndScience]

You are very welcome!

[@Carlos-qz7ul]

Brilliant! ❤ Mr. Jason has me levitating as a feather over a canyon...

[@simpleman283]

Me too, no doubt. I worked 5 days, on understanding the proof at the end. Today, it clicked & i've got that same feeling.

[@namazovmath3372]

❤I was waiting for this.Thank you very much

[@bymoviestube9202]

Ur the best explaining teacher both for math and physics. I've subscribed scince I was elementary and your slow step by step way of explanation helped me experience the early world of math and science without stress or fear. I really mean it when I say 'thank you'.

[@simpleman283]

9:40 first problem. 16:23 negative times a negative = positive. My mind tells me this really is subtracting a negative 689.4, which makes it positive. 30:50 31:55 "make sure you understand this before we go on any farther" Well it took me 5 days, but I fully understand it now.

[@molirathod1407]

Nice teaching sir ! 👏👏👌👌

[@vinuVA]

We don't all have to be students to learn, all we need is interest and willingness to listen.

[@MathAndScience]

Great advice. Love this

[@animeislife6428]

you are the greatest teacher for us

[@efremtse6518]

Thank you so much you teaching me a lot.

[@Guran998]

He makes it so much easier 😮😮

[@miguelvenegas4172]

Absolutely amazing teacher!! Wow.

[@HeavenlyPress]

17:38- that entire tools section was immaculate

[@MathAndScience]

Thank you so much I appreciate it!

[@junmaclan26]

Wow! Thank you so much Jason.

[@MathAndScience]

Welcome!

[@gustavogaviria7678]

Hello Jason, please let me know how I can contact you as I have some questions regarding the paid membership.

[@racksvere4726]

thanks sir 🙏🙏

[@and4563able]

When will these lessons be posted on the website?

[@WahranRai]

the theorem of Pythagoras is for the right triangle, for other triangles the law of cosines or *Al Kashi* 's theorem

[@simpleman283]

This is good, I've been working on law of Cosine & Law of Sine. Me & my calculator are not the best of friends just yet. I got the first one right, but it took me 7 minutes.

[@MathAndScience]

Remember fast isn’t the best. I’m not fast either.

[@davidwarui2073]

Lovely,just lovely listening to you teach calculus and marval at understanding what I didn't while attempting chemistry in 78

[@simpleman283]

31:55 "make sure you understand this before we go on any farther" Well it took me 5 days, but I fully understand it now.

[@4everThoughtful]

That's the spirit!! There is no learning math without a struggle. If you're not struggling with it, you're not learning it; or you already know it. Awesomeness!

[@simpleman283]

@@4everThoughtful Thank you so much for the comment. After working on that problem a couple days on paper, I tried working it on my mid sized whiteboard. Frustrated at not being able to solve it, I placed it where I could see it even while watching videos. I would look at it from time to time. Then I noticed another way to try. Just a couple times doing that & I had it. I really feel like the whiteboard constantly being visible and not being in a classroom rush was key. It was such a feeling of victory, I had to make a comment.

[@4everThoughtful]

@@simpleman283 I'm sincere in my joy for you. Math is indeed a language and it DOES take persistence. For those that never got it, it's because they gave up; didn't want to struggle. The brain is an awesome muscle and it needs exercise to give you the results that you want. I, too, love a large board that I can write on in large print & see it often.

[@drumtwo4seven]

Nice 👍

[@oo-pi2dq]

Thanks ♥︎

[@tresajessygeorge210]

THANK YOU... SIR...!!!

[@nestorsantiago28]

I am learning.

[@niyonkuruidrissa2346]

10x for your commitment sir!

[@MathAndScience]

Thank you!

[@cicerochen313]

awesome!!

[@bobaprakash8905]

You are awesome

[@MathAndScience]

Thank you!

[@liasitumorang6041]

Thank you sir, GBU

[@freepilot7732]

It seems to work for me. I only remember the last one. I just retitle the triangle.

[@eipimath]

Thanks for sharing! I posted a short video on deriving the law of cosines, It should apply for all angles (acute, obtuse, reflex, negative). Hope to get your thoughts.

[@bidarvandi]

you are a light in Darkness(ignorance,blindness)

[@vlad_makes_stuff]

Why are the smart channels like this one less popular than the not-so-intelligent Mr.beast and Skeppy? Reply down below!

[@simpleman283]

Because channels like this are for people that seek to better themself. People flock to those channels you mentioned because they have no plan for their life, they just want to be entertained.

[@shaunalem4810]

Normally people do not like to think critically, so more of entertainment 🙄 world. But this kind of channel requires critical thinking, at least basic thinking to comprehend at least for minutes. So they don't prefer this much.

[@treesajoseph9255]

🥰🌹🥰🥰🥰

[@Blippa-v4x]

More of this "right?" too many times. Ends up being annoying as far as presentaion skills. Perhaps knows the topic but don't know how to present it well. "stick with me" means I know I over-explain and you guys already got it but I keep saying it anyway.

[@brucea9871]

Good video for those unfamiliar with the law of cosines (although I learned it a long time ago; in fact I taught myself trigonometry from textbooks long before I learned it in school). I do have a few suggestions though. First it's a bit distracting (for you and your viewers) for you to continuously read your notes before copying them to the whiteboard. I could write virtually everything in this video without referring to handwritten notes (the exceptions would be things like finding cos 20° and multiplying it by 2ab). For things like that maybe you could have notes posted just off screen. Second you do not really need three separate formulas for the law of cosines. Instead of having separate formulas for a squared, b squared and c squared we could just relabel the sides of the triangle (e.g we could relabel side a as b, side b as c, and side c as a). Or we could use the general rule you mentioned. The square of any side of a general triangle is equal to the sum of the squares of the other two sides minus twice the product of those two sides and the cosine of the angle between them. Third you could have mentioned the law of cosines can be used to determine the angles of a triangle if the three sides are known. All you have to do is solve the law of cosines for the cosine of the angle and then use the inverse (or arc) cosine button on a calculator to obtain the angle. But perhaps you omitted that to avoid making the video too long. I am glad you included a proof at the end. Although I've seen the proof before others may not have and I think it's a good idea to know where such formulas come from and not just blindly believe them.

[@simpleman283]

Critique your own video, Oh your channel doesn't have any content. How very interesting of you Professor.

[@MathAndScience]

Any university professor will have notes they lecture from. I’m not blindly copying them. It’s to ensure that I say and talk about every topic. If I didn’t have notes I would inevitably miss something. I doubt you could memorize a 30 min lecture. Believe me I have tried that. Again, go to any college class and you will see professors with either slides or notes they lecture from. Thanks, jason

[@brucea9871]

@@simpleman283 That's as ridiculous as me telling you to critique your own comment. I will critique any video that merits criticism. Essentially you're saying we should not criticize anyone but ourselves which is ludicrous. I am not endorsing criticism just for the sake of criticism (I've seen far too many people do that) but rather constructive criticism so the recipient of the criticism can improve.

[@simpleman283]

@@brucea9871 No, you are ridiculous. You have NO constructive criticism so, leave the teaching method to the one that doesn't need your help.

[@simpleman283]

As soon as I read you telling him to change the sides of the triangle, rather than show three formulas for the Pythagorean Equation, I knew you do not understand the importance of students recognising patterns in math. Therefore my comment, Bruce.