05 - Sine and Cosine - Definition & Meaning - Part 1 - What is Sin(x) & Cos(x) ? 

If I had you as my math teacher in high school, my life would have gone to a different direction. Clear & Simple.

I'm a happy 75 year old. Thought I was math-hopeless. I got this lecture totally. Wish I seen this 50 years ago.

As a fellow math teacher, I can say that this is an excellent video as he does a great job of explaining the ‘WHY’ of the data. Well done.

I'm almost 70 years of age, and working for 5 different major oil companies early in life, the pipe trade in fitting requires knowing right angle trigonometry, this is a powerful math to know, it will reward you greatly to learn it.

Amazing content every single second was full of important information and it was so well explained!! Thank you for uploading these lectures for free💖

This world needs teachers like you. You are just diamond. Thank you very much for your knowledge for your passion for your time.

If a man keeps me interested over 40 minutes in something that I have no idea what’s he’s talking about it’s because the man knows what’s he’s talking about and suddenly trigonometry feels right. My respects to this teacher.

I was intrigued and now wish I had this understanding 45 years ago when I was in school.

If everyone had a teacher like you we'd be living in a much better world

if you define the hypotenuse of a right triangle as 1, the sines of those 2 other angles are the lengths of the legs opposite the angles, and the cosines the length of the legs adjacent

This man is legend! I used to watch and learn from his calculus teachings and his videos helped me a lot while in college although he was young man that time, 13+ years ago. Thank you for teaching.

Just realised I wasn’t dumb my foundation was weak af

We only learned how to use Sin and Cos. Finally, at the age of 61, I have finally understood them. A massive thank you.

I have watched so many people here teaching sciences but but the way this guys explains these chapters is awesome, way aboooooove others. His accent is very easy for me, and the formulas other teachers come and throw on the blackboard this guy explains them from their beginning and how they came to life. I simply loooooove his methods. Thumbs up, man!

This lesson should be the very first subject on all math subject text books. All teacher should learn this too. Great Mind think simple.

I learned with this lesson more than the whole time that I studied in high school, even in the College. The teacher has a great examples to show how its would be easier to student figure it out, for me it was that I almost see the vector was moving.

Small correction: If the hypothenuse is 5, that does not, by definition, mean the other two sides are 3 and 4. Which is what you seem to imply at around 5.20...... Let the hypothenuse be the radius of a unit circle, r=5. I can now rotate R and subsequently construct an infinite number of right triangles, hyp=5 but with varying lengths of the other two sides. A 3-4-5 triangle is just one of many possibilities.

Good Lecture. One observation: from the Physics point of view, when you decompose the 5N force into the horizontal and vertical components, these components need to have the same origin ... also common with the 5N force .This would also help when you use the projection on the y direction.

where was you when i needed you at school in 1952....brilliant thank you......

I’m 72 years of age. I can only reiterate Halbert Thomas. “ I got this lecture totally” I’m addicted . Many thanks

If only you were my instructor back at school, I may have enjoyed and eventually got a passing grade in math! I love all your videos! I never got to trigonometry, but you make it understandable! I love it! Thank you!

We learned this as SOH-CAH-TOA. Sin is opposite over hypotenuse, cosine is adjacent over hypotenuse and tangent is opposite over adjacent.

I really enjoyed science in school. I was good at it but Trig Stopped Me! I got an A+ Precalculus but I couldn’t move forward. I could never understand sin and cosin. After wasting so much time, it only took a 45 minutes video from someone I didn’t pay a cent to get it. Thank you so much sir.

I'm 55years old lady I love maths very much even at school. I never think in my life I will understand maths the way I am now. Thank you so much for refreshing my mind even for others at my age. I enjoy this too much . May God bless you with many more years

when i was in the school, i really hated math. but when i'm watching this, my hate reverses becoming love feeling.

Thank you! Old textbooks were simple and basic lessons, with a history lesson of why you were doing something. I’ve been buying early 1900’s university books off eBay. These new books have way too many pictures of panda bears and no reasoning for the lessons...

chopping function is really out of the box. Thank you sir.

I've been a professional programmer for over 5 years. Software Development, so you generally don't use a lot of math like this. It's much more about collecting and showing data ina certain way. I've dabbled in game dev in my spare time and I can get pretty far. But a lot of it is looking up math functions for something, but not truly understanding what it does. It gets the job done a lot of the times, but I feel like I got stuck and not be able to progress and get my own answers to problems. Now I decided to go back to the beginning and truly try to understand vectors, trigonometry, dot product and cross product etc. I always get stuck on trigonometry because it's never truly explained what sine and cosine do (only how to calculate it). This video is incredible, especially understanding it and why its so powerful as a fundamental concept in game development.

This was a helpful refresher, your stick figures "third leg" gave me a giggle as well. Thanks!

You deserve a place in Olympus, man! Really, I have studied even calculus I, but I have thought that the sine and cosine are respectively the y component and x component always. But, you have demonstrated that this is true only when the hypothenuse is equal to one, because of this I messed the things up, unable to understand why the functions are constant whereas the components vary. Thank you very much!

Very clear thank u. I am 68. I had a very similar math teacher who got 99% of students passed A level maths. Best teacher ever

Why is 0.8 (cos theta) + 0.6(sin theta) greater than 1 if it is a ratio of Total Force? Shouldn't the total be equal to 1? if not why?

Making Trig this digestible is amazing. I often don't grasp math unless I thoroughly understand why and how it works. My biggest pet peeve is when people say "just follow the formula, you don't need to understand." Before this video I had such anxiety when it came to trig, but the way you have taught it is clear, concise and comprehendible, not to mention the enthusiasm while doing so. Your videos are very admirable, my university needs a prof like this!

I am 70+ years old and hold a degree in Electronics Engineering Technology. To work in the electronics field, it is imperative that one is well versed in trig. This man is exceptional with mathematical skills. See below how I taught trig functions to my boys when they were having trouble with trig. There once was an Indian chief named SOH CAH TOA. He thought for a long time how he could get the maximum distance out of his arrows when he was hunting game. Then one day as he was putting on his war paint =/ =/ the answer suddenly came. S=O/H C=A/H T=O/A. And so it was that trigonometry came to be.

I remember exactly as this guy told, A light bulb 💡 lit 🔥 when I was solving problems in vector, oh that’s what cos n sine are.... There is a nice video of RP Feynman telling how mathematicians don’t explain things with physical meaning when they teach... that’s not tangible for human brains while learning...

Question: how do you explain the sum of component forces is bigger than the total force ?

After this video, my hair and beard turned white and I had a stone tablet in each arm. One called sine and the other called cosine. Amen.

I will definitely show this video to my son who's just started high school. Just a fantastic video! Thank you!

Thank you for making the world a better and fun place to live. I am so happy to watch this video again and again. Now i can see the Sin Function and Cos Function in all my movements of house keeping, cooking, gardening, star watching, exercises, leap and jumps. I can visualize the "Chopping Functions" in the sound wave of children's laughs. Now I understand why "Math is the queen of science". Thank you, thank you, thank you... for making the world a better and fun place to live.

“This is what they’re for….” Should be the second sentence spoken by every teacher of every course following the name of the course.

Oh myyyy Im waiting for thissss thank you so muchhh sir Jason....god bless....

Best video about trigonometry on entire RU-vid. Thanks for thr efforts sir.

Absolute genius as a teacher....Every student should insist that their teacher is as good as this... Me? I'm simply thankful for this.

I never thought I could find math relaxing but this really is captivating. Thanks so much!

Never seen this guy before, im 2 mins in and already committed to watch this through to the end. Why was this guy not my teacher in school!

"I'm terrible at drawing", he says as he draws a three-legged man. I think it's anatomy you need brushing up on, not drawing XD. Great channel though; watched a few videos and they're very helpful!

Solved sine cosine, after 25 yrs, thank you sir.

This is by far the easiest I've ever had this explained. This is understanding at the base level so it's not only hypothetical like most math teachers' explanations

Sorry my secondary school teachers what was try to teach is this. Such brilliant explanations. I'm in great sorrow for the time loss to understand this. Lots of teachers must learn from this man. Finally all these are related to the force thing. Thank you for your amazing effort for evolution of intellegence.

After watching this video I have realized how dump were my teachers in the school and in the university as well .i knew something was wrong and I thought it was me 😁.Thanks a lot

It makes sense of what these ratios mean. You are something special.

I'm 74 years old. Hobby is woodworking and I still use trig, but this was the first time that I truly realized the "why" of those numbers. I like his description as the chopping function.

i am a 50 year old dad and i learned it again so i can sit with my child n explain it to him while we watched this video togather... thank you so much.

Your diagram illustrates the components of a roof pitch, which is a combination of the horizontal run, and the vertical rise. So if you had a 4/12 pitch, a 12' run would rise 4'. Since it is describing ratios, it can be reduced to 12 inches of run and 4 inches of rise, which occur simultaneously. And if the pitch was 4/12, but with a run of only 8' (or 96") the rise would be 2' 8", or 32", which is one third of 96', in the same way that 4 is one third of 12. I'm not sure if this has anything to do with sine and cosine, but I was struck with the similarity to determining roof pitch.

Thank you for explaining this in such a manner that we can "understand" this vs "know this".

I'm 13 I was failing maths then this channel was recommended ur a blessing man I passed math for the first time and i was ecstatic your really great :)!

I wish I had this guy back in high school 20 yrs ago - I could have actually studied engineering instead of being stuck in shit jobs lol. But here I am in my mid 30s at Uni having to learn parts of stuff I never even learnt in school properly. And I find myself scrolling thru RU-vid for decent videos since all the lecturers assume you know this stuff lol. Thankyou, Sir! Seriously Thank-you!

I took Pre-cal about 10 years ago, and now I've been blessed to be able to go back to college. This is the first time I've ever been able to understand what these terms actually meant other that in some formula that was shoved down my gullet to regurgitate later on a test.

The way the teacher delivering and illustrating is fantastic 👏

By God, I never saw a this kind of teacher before , lots of love from Pakistan Bold and concept way of teaching,SIR. Hatttsss off.

BC: If I got him 25 years back, I would have been working in NASA.

How I passed physics when I was in college years ago with a respectable grade, with zero understanding of the reasoning for sin and cosin is beyond me. Maybe because I just watched this video for the hell of it, just in case I ever needed this info, which I won't, but I know it and that's all that matters! Lol.

I actually understand this, first time in my life. I wish I had him for a teacher when I was in school. Great video.

You make things so simple, I send your videos to my students!

Such excellence makes me unable to hold expressing my appreciation.

Very interesting. I am 80. Been maths teacher at secondary school . I enjoyed the class.thanks.

You sir are a lost art who would be canceled and the days education system I appreciate what you just showed me thank you

He is the be best of OF a teacher's I know all of my SCHOOLING YEARS.. He is the world's best I can attest.

I am really thankful that I saw this when I am just a kid. I understand a piece of math language. Thanks.

I feel like I should be paying this guy $326 per credit hour. There have been some definite holes in the information I'm getting from my college professor and he filled in the gaps. THANK YOU!

A minute and a half in I'm very much looking forward to the rest of the video!

I have never been a math nerd but I really love this. 1. In effect, we're measuring quantities of force exerted through measurable distances of space. The lines are simply visualization aids - we are not measuring lines. (Light bulb moment) 2. If 40% of the force is identified in the x-axis and 80% in the y-axis you have identified 40% more force than there is quantity of force available. How is that possible? Shouldn't Sin + CoS = 1? 3. Force, like wind, is invisible and intangible only its effects are observable and measurable. What is force?

As a student looking for a review from the ground up this is perfect. I personally was having difficulty conceptualizing some trigonometric things within the unit circle, this is a great gateway into that thanks!

This is not my native language but was the best teaching I have ever experienced on this topic despite the language barrier.

Thank you Prof, I am 71 years old and, for the first time, I understand what Sin and Cos mean, rather than learning it by rote. Wish I had known this years ago, but hey, never too late,

I am in love with this guy, his knowlege and his way of teachings!

He is great. His enthusiasm and passion for the science is contagious.

The stick figure's "third leg" is distracting me.

Thankyou so much i feel so confident after your teaching.. the way he teach feels so easy like when i was in 2nd grade

Very good effort to make it more and more comprehensive.

Im in 10th grade, I didn't understand any of these trig functions and saw them as useless. Thank you for making me see the true potential and usage of these essential functions and ratios. Huge respect from India sir!

it's really hard to be a bad teacher, it's even more difficult to be an excellent teacher. you can truly tell the difference between one who values their knowledge and is excited to share it, to those who just kind of like teaching

You are very talented 👏maths teacher. I was always the best math student among my classmates in primary schools, secondary schools and technical institute. As I study mechanical engineering back in the late 80s I wish I had a lecturer with your abilities to teach maths. You are amazing 👏❤

Not only are you a talented teacher, but your diffused lighting is on point. No annoying shadows or glare on the white board. Thank you.

“When the student is ready the teacher arrives”. I’m 68 and finally am ready. Thank you teacher!

My teacher on internet.. big salute to you sir

Wow. Always wondered. Now I know. Excellent. Wish I had you for a high school teacher.

I too am 75. All this made a lot more sense ( not just memorizing) than it did many, many moons ago.

If every teacher, for every subject, on every school, will follow your statements on the first 2 min of this video..... OMG It will be a different world in educations and progress.

wow finally it really clicked. and i totally agree with Halbert. I mean i'm not his age but i wish i've understood this back then in school just like now. thank you so much.

We need a teacher like you in our college

If you’re young now. You don’t understand how lucky you are to have stuff like this on RU-vid lol

I bombed trig in high school. Okay so I was bored and confused. But this guy makes it sound interesting and simple. Great teacher.

Best tutorial I have ever watched!!

Excellent. Falling in love with Maths.

Thank you for this explanation. You have made this much more tactile for me. Thank you so much.

During my geo/trig and pre-calc classes these terms were mentioned but I never actually knew what it meant. This video was exactly what I needed. Your method of teaching should be praised. The way you repeat the same concepts throughout the video, and go back to previous problems helped emphasize main ideas or your so called "punch-lines". Thank you.

This is the epitome of a great teacher.

I learnt this in school but never knew how it was useful in real life. Now I do.

I am a software engineer and for fun have created a cube rotating in 3D with objects within it. I found an example of a simple rotating cube that I used that made use of sin and cos to calculate the rotation. It all works which is good - however I want to learn again what these two function are. Great talk!