05 - Sine and Cosine - Definition & Meaning - Part 1 - What is Sin(x) & Cos(x) ?
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- čas přidán 22. 06. 2020
- View more at www.MathAndScience.com. In this lesson, we will learn fundamentally what the sine function and cosine function represent. We will learn that the sine function, also written as sin or sin(x), reduces the hypotenuse of a right triangle to the projection onto the y-axis. Similarly, the cosine function, also written as cos or cos(x), reduces the hypotenuse of a right triangle to the projection onto the x-axis. Thinking of sine and cosine as projection functions like this helps us to visualize exactly what the sin(x) and cos(x) functions do. This has applications in math, engineering, physics, and all branches of science.
I'm a happy 75 year old. Thought I was math-hopeless. I got this lecture totally. Wish I seen this 50 years ago.
It's very nice
Thanks so much, I always wondered what sin cos tan were
Me toooooo
Awesome!
You are confusing math with teachers that only know what the book says the answer is, they are hopeless.
If I had you as my math teacher in high school, my life would have gone to a different direction. Clear & Simple.
In several other first world countries you would have had a math teacher like this, but it would’ve been in late elementary school, not high school. This hypothetical teacher would not have had union pressuring the state to hire only education majors, excluding math and science majors.
omg ikr??? maybe we would be nuclear scientists or something.
I had a teacher like him in high school. Mr Nelson, Medford High, Medford MA.
You had a teacher like him in high school. You just weren't ready to learn when you were in high school.
@@speedoflight3395 Are you a Nigerian who practices Vudoo?
I'm 65 and taking college trig right now. I haven't done any trig for almost 50 years and these videos are like a breath of fresh air. I learn something better if I know the why and not just the how.
Keep on Old timer.
Good for you. It’s great to be lifelong learner
Dear Teacher, I am writing to inform you that for the first time in my life (I'm 55 years old), I have finally understood the Trig functions concept. I have read a million times, over the years that the angle sin0 is Opp/Hyp, but I have never understood what the heck everyone was talking about until I watched this videos. Everything fits into place for me now. Why am I even watching this video at the age of 55? Well, my daughter is struggling with this concept as well. I wanted to revisit the topic and see if I could help her. I am glad I found you. Over the years that I have watched your videos, I think you are the most effective teacher I have ever seen. The concept of "chopping factor" is a miracle. Concept this simple, I don't know why the teachers can't really explain it clearly to their students. Could it be that they themselves are just repeating what they memorized, without any understanding?
Thank you for the incredibly kind words!
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.
How can you put in 5N and get out 4N and 3N?!
If I had to build a dye requiring a 4N force right and a force of 3N up.. could I achieve that?
If that is true, then wouldnt a magnetic force also work along the same principle and be proof for over unity?
@@hychap idk if I'm understanding what your confused about right but, you put in 5 as the hypotenuse of a right triangle and since it's a right triangle the other sides have to be 3 and 4
@@cottoncandycloudsrobloxedits No they dont, the lengths of the legs can be any of an infinite number of lengths if the hypot is 5.
He just CHOSE a 3/4/5 triangle as an example
@@ronalddump4061 oh sorry I'm just learning this so i must've misunderstood
@@cottoncandycloudsrobloxedits Obviously if hypot is 5 one of the legs can be anything between 0 and 5, right? That is an infinite number of possibilities. He just chose the 3/4/5 for convenience. Round numbers
I almost didn’t graduate high school because of math. I slipped behind once and never caught up again. Fast forward, I’m 22 and I’ve decided to spontaneously pursue physics. I watch your videos religiously. I didn’t realize how highly intelligent I could be with the correct teacher. Your work is very much appreciated thank you for your quality and dedication
Woah !!! Amazing, we're in the same boat!
The state of education in America is much worse 😅😄
@@yuvraj9797
how come😂
Me too
I'm a mostly happy 88 year old who had major problems with math in high school. You, sir , broke through a lot of ancient haze tonight for which I'm grateful since I can "assume" that maybe I'm not as dumb as I thought ! Thank you for your patience and clarity in explaining sin and cosine.
Just for interest, I started a STEM degree at 49 and now we're onto maths, which was my least favourite subject at school. This has been very helpful. Seeing cos, sin, etc. being described in such a practical has made it so much easier to learn. Thanks. I wish we'd had CZcams in the 80s!
I’m pretty sure most observers feel that they would have had not only a better understanding of the subject, but ,also would have enjoyed the lesson and presentation.
This gentleman was born to teach.
Humble and erudite..Bravo!
This world needs teachers like you. You are just diamond. Thank you very much for your knowledge for your passion for your time.
No, this country, which is behind most first world countries in STEM education, needs THIS teacher to replace the education majors who cannot teach a subject they themselves do not understand. Instead of the unrealistic goal of having thousands of teachers like this one, broadcast this lesson into thousands of classrooms replacing ineffective teachers. Much better results at much lower cost.
👌👌👍👍👏👏
I know you are saying this with a good intention but diamonds arent expensive or rare , they are actually more common than you think . Their market value is high but their actual value is so much cheaper than that
He is the best at his topic. I wish he could also break down calculus and simultaneous equations into their intuitive versions. None of us is bad at math I am realizing. It is just how we r taught that messes us and bruises our confidence in the process.
@@stevekru6518 not most classes possess smartphones or even data.
I’m 72 years of age. I can only reiterate Halbert Thomas. “ I got this lecture totally” I’m addicted . Many thanks
Welcome!
I'm in 8th grade preparing for next year and you are somehow able to convey these concepts to me perfectly. Thank you.
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.
Fantastic stuff I really enjoy math like I have never before ,I used to be bad in trigonometry but now it's a different story
Attention deficit is causing the problem
So rectify ur attitude
Thanks 😀😂😂🐒👍⛵💯
This is amazing. You are a very talented teacher. Your dedication and passion shows in the high quality of your work.
Thank you so very much!
@@MathAndScience ppp
Very clear.
I second this.
Thank you sir for such a comprehensive lecture.
@@MathAndScience p]
When I was a kid in Glasgow, I was sent to Secondary school a year and some months early. I was put into "Prep A" and I was taking math, chemistry and physics as well as the usual classes, English, Art and Music. I was put into a course with a few other kids, called "New Math" . The only problem was major. I had never heard of anyone being sent "ahead" so I took it as rejection and thought my teachers did it to be rid of me, because I was the boy with the problem, I asked too many questions. I was also from a poor working class family and had to leave school to work at the earliest opportunity. I knew that but my teachers didn't.
I had to leave at 15 yrs and I went to work 6 days a week and gave my wages to my mother. I was the sole support for my mother, myself and two brothers at 15 years old.
I am 69 now and still read educational and scientific materials all day, every day. I wish I could sit in on university lectures and just learn
I never understood why we use these functions. Finally someone who can explain "the why of the trig functions." Excellent explaination. Impressive!
I'm still confused at everything
I m 45 years old I love Math but really I wish we had CZcams on our days 💔 I keep watching your videos till 4:00 am they are much enjoyable than Netflix 😇
dude, have you seen Breaking Bad ?
That sounds like me, why watch distractions when you can learn/do. 😎
@@roysmith3198 said no one with ADHD ever
Poor me. Now 83 ,but in my teenage schooldays had to learn maths not undertandin
@@pcchin3920 not to worry, the lucky part is you came upon this video at the right time. Nice calculus!
With access to this high quality of educational content online, poor third world like where I live might finally get a chance to compete. Thanks mate.
The internet has really leveled the playing field for educational opportunities around the world.
The US ranks poorly among other first world countries in primary and secondary STEM education. The US needs this educational content to replace education majors who cannot teach what they do not understand
@@stevekru6518 You said it!
Try my channel mathfullyexplained. Full unit on right triangle trigonometry plus more units
Never imagined I'd be an exbricklayer watching a math video for my own enjoyment on sunny Saturday afternoon but here I am.
Best video about trigonometry on entire CZcams. Thanks for thr efforts sir.
I was intrigued and now wish I had this understanding 45 years ago when I was in school.
Thank you Gordon!
It is unusual for someone who is 69 yrs old sitting in the late evening at his home in India, watching this. Despite the drawback of catching up with the speed and accent (i relied on CC), I really felt that I would roll back to 55 years and sit in my class again and listen aptly the mathematical jargon. I really remember my high school Maths teacher talking Sin Teta and Con Teta and forced to learn those things. I would love to be a Maths teacher...but...you know, I keep listening to you as to when youtube obliges me. Thank you, Sir.
You are very welcome!
Remember you can also slow down the playback speed to 0 75 if it helps.
Very reliable and sincere. Thanks.
If everyone had a teacher like you we'd be living in a much better world
The grasp this man has on his discipline is remarkable. He mastered, he educates. Most educators skip the first part. Thank you for helping us 🙏
His passion and energy is contagious. Excellent teacher.
Encouraging manner in such an otherwise difficult subject matter.
We only learned how to use Sin and Cos. Finally, at the age of 61, I have finally understood them. A massive thank you.
Try my channel mathfullyexplained. Full unit on right triangle trigonometry plus more units
Im 40 years old with MBA degree , i never knew what is sin and cos are until i watched your video. Why teachers are not like you in teaching . Very much appreciated the way you teach . Thanks 🌹🌹🌹
where was you when i needed you at school in 1952....brilliant thank you......
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 CZcams for decent videos since all the lecturers assume you know this stuff lol.
Thankyou, Sir! Seriously Thank-you!
Just realised I wasn’t dumb my foundation was weak af
Exactly
same
Nobody is dumb
@@chrisromero5302 i am dumb
Dumb is just a synonym of lazy. Nobody's dumb, some are simply more motivated (smarter) than others.
That's the best explanation of the sin cos ratio set up I ever heard...brilliant and thank you ☘️😊❤️
Awesome thank you very much!
Try my channel mathfullyexplained. Full unit on right triangle trigonometry plus more units
Amazing content every single second was full of important information and it was so well explained!! Thank you for uploading these lectures for free💖
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!
At my school in Drumchapel, Scotland in the sixties I was completely confussed by trigonometry. After this lesson I now understand the meaning of Sine & Cos and now I just want to learn more from you to prove to myself I was not really the dummy I thought I was. Keep doing what your doing, it makes a big difference.
Your trig class showed you all this material. You just werent ready for it, or didnt care. Generally at that age all people are typically thinking about is the hairy end of a belly
@@millicentsmallpenny5837 hell nah even tdy this material isnt shown in school, no way it was in the school system of the 60s
Incredible! 60 years ago my math teacher was unable to make me understand sin&cos and I stuck with Pythagoras! Thank you so much for finally making me getting it at 75!🤗
This is the best lesson on sine and cosine I have ever seen. I've been using them for years. I really wish that I had a teacher like you back in high school. Congratulations!
Our world can definitely use more people like you. Keep up the outstanding work.
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
I graduated A engineer but I can say that I never say math made so easily to understand. I wished most math professor were like you. More people would definitely love math.
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.
For 72 years I have been mouthing SINE& COSINE without knowing what they actually mean OR represent!!. Deep thanks for I am now happily enlightened.
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.
awesome explanation. Yes, I wish I had him in high school. You can hear the love of what he does in his voice.
This teacher is awesome! My math teachers gave us tables, formulas, equations and said memorize them and use them! With very little explanation.
Here's proof that a GOOD teacher is a country's greatest treasure!
I finally got it. Thanks a lot. My teacher in gaza, palestine made me memorize it, and i didnt understand what i memorized and why I had to memorize it. Now I am 45 years old and I understood. Thanks a lot. You are the best teacher ever
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.
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.
You can construct an infinite number of triangles. Only one of those is right with a hyp of five though.
Only the 345 triangle will be a right triangle. Change any the lengths of the sides other than the radius and you don't have a right triangle.
Thanx I was just scrolling down to see if anyone had any info on this, and here it is.
😖
@Ca Study sorry you are wrong and so is the teacher. The opposite could be 1 and the adjacent could be the square root of 24 for example. Use Pythagoras' Theorum. In a right angled triangle the hypotenuse squared = opposite squared + adjacent squared, so with a right-angled triangle with a hypotenuse of 5 can have any lengths of opposite and adjacent whose squares add up to 25. 3 and 4 may be the only 2 whole numbers whose squares add to 25 but there are an infinite number of non-integral numbers of values greater than 0 but less than 5
I thought I am learning math in the class in person with a teacher who is passionate what he is doing. Thank you so much for your time and passion!
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’m in 8th grade and I want to learn early so I don’t stress when I’m older. I also code a lot so it’s helpful!
Bruh good for you kid, when I was at 8th grade I wanted to learn Calculus so that I don't stress out learning. But turns out my knowledge is far left behind. Now I'm currently in 9th grade lol, currently discussing Trigonometry. Goodluck!
You'll forget more than you retain. Don't stress it pal
@@jackhoff7880 thx
No need to stress! The beauty of math is it is totally logical and consistent, unlike most of your other classes. All you have to do is learn the rules, do some homework, and you will succeed. I disagree with the comment that says you'll forget it all later. Once you learn math, you can devote your life to science or engineering and help humanity. I'm a 70+ year old chemical engineer and I've used this stuff my entire life, even in my woodworking hobbies, and so much else (I also code as a hobby).
The magic of math is it develops the parts of your brain that think logically, instead of emotionally. You will see the world and the universe differently when that brain muscle has been developed and exercised.
What do you use to code, Arduino?
There's another GREAT utube math teacher: Eddie Woo. Please check out his videos on trig (and so much more math) - he's really great.
I used cosine and tangent when I was building houses, to set out the framing for roof trusses, I wasn't interested in this at school, but when I became a builder , it came in very handy .
Me too. As a 16 year old I never understood why I was learning this. Now I measure the length of walls roofs windows in architactical drawings and than the software makes a report of energy loss for the co2 problem in this world, every new house must have a report like this now.
This practical knowledgeable shouod be transferred to people who are trying to learn this. Its people like you who must make some videos on this with demonstrations. Would be much easier and quick to assimilate the concepts.
Same
Basic program to draw a circle (I learned it at 14!)
1 cls 'clean the screen
10 for n=1 to 360 'counts 360 degrees of the circle
20 plot 320+100*sin(n), 200+100*cos(n) 'draw dots of the circle centered at coordinates 320 x pixels, 200 y pixels, and a radius of 100 pixels
30 Next n
40 end
Do you want to try it? Download winape amstrad cpc emulator, type the program pressing enter or return at end of the lines and then typing run and typing enter or return again, you will see the circle being drawn dot by dot on the screen of your computer, want a filled circle ? Add 15 plot 320, 200 and change the 20 plot command in 20 draw using the command edit 20 command and [RETURN]
1. CLS does not mean CLEAN the screen, it means CLEAR THE SCREEN
Go to a CLI and type HELP , Look up CLS and you'll see the description CLEARS THE SCREEN
2. What is the programming language.... BASIC or something like that ?
@@martinkuliza sorry, you're right...I 'm Italia and I was confused by the similarity of the two words. It is locomotive basic, the basic used in the amstrad cpc 464 you can find a simulator called winape
@@Thebasicmaker
1. OK, No Problemo
2. I've never heard of Locomotive BASIC. I'm from the old days of the commodore 64 and Atari Generation , i grew up on BASIC V2
64K Ram system Ready :P
that's why i recognized the BASIC code (not that it's hard to pick)
3. Just for fun, I'm currently reverse engineering a ZILOG Z80 CPU . it's quite interesting
i thought i'd mention it since you brought up the Amstrad
4. I'll check out Winapd, thanks
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'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.
This was a helpful refresher, your stick figures "third leg" gave me a giggle as well. Thanks!
What's the angle of the dangle proportional to?
@@BradCozine lol. I see what you did there
I was scanning the comments just to see if anyone else noticed the tripod, too. ⚗️🤭😁😄
This man is a genius. He realizes the value of answering the age-old question every wise-ass kid has in school..." when will I ever need this?" It's shocking how many teachers never answered that question. It would have been so helpful to me personally, which is why I'm here now in my twilight years. It is only fitting that a hero of this caliber would be able to lift both feet off the ground at the same time. I wish him length... and girth.
I also came across sines and cosines at school more than 70 years ago and I never understood what they were before now. Thank you for making it so clear.
just out of curiosity! what made you come to math again?
Damn !!! This is the first time Ive understood this subject. You got the talent to teach this subject that most Math teachers dont have, and thats a fact . Im 75 and I finally made sense of sine and cosine. Id like to hear the rest of the Trig functions explained AND applied . Thank you ! I always want to know the WHY of math concepts, but no one has ever explained them. Now someone HAS !
Phenomenal. I’m helping my 14 year old grandson with his trigonometry. He could do it but I could tell he didn’t know what he was ‘actually’ doing. I found this video and we followed it together…pausing so he could rephrase the points in his own words . Now he ‘gets’ what he is doing.
I aced math throughout high school and second year Calculus in university. . Confession, I had no idea what I was doing until I had to apply it as a geophysicist. Your 48 minute lecture would have been invaluable when I was my grandson’s age… the better understanding, the more fascinating math becomes instead of a hurdle to get over. Most importantly, my grandson now has a positive towards his math class.
Calculator? Ha! I learned using a slide rule and tables.
Thank you so much. You are an awesome grandpa!
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...
Yes I agree!
The practical application is really what people want to hear, very few have the love of theory. Keep up the good work.
They call it common core
Try my channel mathfullyexplained. Full unit on right triangle trigonometry plus more units
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!
Being a PhD in mathematical statistics, this is the first time I understood what the sin and so are. Salute to this huy. related subject
This guy is a King at explaining math and science. (having an engineering degree instead of just being a "math professor" probably helps too. I was here just for a refresher.
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.
when i was in the school, i really hated math. but when i'm watching this, my hate reverses becoming love feeling.
Releases the fear factor memories releasing endomorphins. !Good for you
I wish your English language hate reverses too :) jk
@@mustafaali-wp2nu -_- bruh
Love watching you from morocco .
You just saved my life to make my son understand sin cos tang .
Solved sine cosine, after 25 yrs, thank you sir.
To quote a previous question - -" when you start - if I am pushing with 5N
and that force divides into 4 n and 3n - if I could extract those forces seperately I now have 7N total -"
HOw can one get 7 N of force from 5 ?
I would realy,realy like an answer
Same question
I am thinking it has something to do with pythagorus.
My question too!
I knew someone else would have noticed this also. Any answers yet?
It is a bit more nuanced than that. What it effectively means is that if you push with 5N on that angle for lets say a distance of 500m (calculated diagonally), it is as if you pushed first horizontally with 4N for 400m and then vertically with 3N for 300m. This is the reason why the values cannot be "directly" added, because the split of 5N into 4N and 3N does not mean that the two resulted forces are applied for the same diatance as the original one.
We could get the same results by calculating in time. The core idea is that the resulted forces are not applied in the exact same conditions, so that is why you cant just add them to get original force.
His explanation mathematically is correct but the way he explained what is going on with regards to the forces is wrong or misleading.
He should have used Joules... but let's go with this. The actual explanation is that the Hypotenuse is shorter compared to the Horizontal (Adjacent) and Vertical (Opposite) lines added together. So if you needed 5N to push the box through the length or distance of the Hypotenuse, you would need more force if you push the box Horizontally first and then go Vertical because the total length or distance traveled is LONGER. So going horizontal and then vertical would require 7N because of the longer distance the box would have to travel. I hope this makes sense.
Loved the way you teach with so much energy and enthusiasm. However, its wrong and misleading to explain the force 5N splits to 4N and 3N. It could have been like 4N and 3N is needed to produce an effective 5 in the 3rd direction.
Furthermore, it is NOT correct to say that if the hypotenuse is 5, the other two sides MUST
be 3 and 4. They may be, but they could also be something else entirely, for example 2 and 4.582.
@@paulhammond61 right triangle vs non right triangle?
@@Herlongian David, all the above applies to right triangles only. If it is not a right triangle then there is no hypotenuse.
@@Herlongian a right triangle with an hypotenuse of 5 could have other sides of length 1 and SQRT(24), or 2 and SQRT(21), The video is completely wrong to say that all right triangles with a hypotenuse of 5 have other sides of 3 and 4.
This channel put out a video with some great information to help people get an understanding of what is going on in a 48 minute video. How long would this video be explaining every little nuance. Splitting N force proper and alternate right triangles with hypotenuse of 5. This is a starting place, and a HUGE help to most watching. You guys coming here critiquing this video have no video of your own.
OMG I was just searching about sin and cosine for my little girl who is in secondary and she is so confused about it. instead I had a lecture for my self. wish I had it some 40 years back. we learnt the formulas and crammed it just to solve questions. knowing the real definition settles everything and last for ever. Master class. Thank you Sir. Salute.
Best Math teacher in world
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.
Can you teach it???
Can you teach me please???
Juan Sulca right ? I wish i had CZcams in my time 😏
Once in class 9th I asked my government school math teacher where these words taken from ? From which language and what they literally means? He obviously didn't know. Felt little embarrassed and then shouted so much that I could never ask again. Thanks CZcams that I am learning this in my 37th year.
Legend!! I wish I had you as my teacher in High School
finally I met the perfect math teacher in my entire life. I would like to see a book from beginner to advanced in maths. please write a book it would be a legacy for you and beneficial to the generations to come.
I am so glad that I found him, he is better than all math teachers that i had! you saved me thanks! keep doing what are you doing!
explained flawlessly, im not even halfway into the video and this is starting to make sense, thank you so much!
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!
Thanks so much! Take care!
That explanation with the flashlight was brilliant, 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.
This guy is brilliant - I wish I had him as a teacher - Now I actually understand what the hell Sine & Cosine are - I've seen them on calculators for years !
Many thanks.....all the way from London.
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.
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 am speechless of what you have done. I really appreciate and it it was the best way of understanding the sine and cosine, which I have never seen it before. Tanks for this great job.
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?
You are mistaken. The identity you are thinking of is (sinx)^2 + (cosx)^2 = 1. If you rise 0.8 and 0.6 by the power of 2 and add them you would get 0.64 + 0.36 = 1. Now to answer your question about force, you should think of these components as two different vectors Fx and Fy. Now try to add these vectors. In order to add them, you would use the Pythagorean theorem. (Fx)^2 + (Fy)^2 = F^2. From this, it should be clear, that the sum of components is greater than the total force. The other way to think about it is to remember when the triangle exists. The sum of any two sides must be greater than the third side. And the components of force and the actual force itself makes a triangle.
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
The moment he explains how trig is applied in physics, my mind was blown. Its intriguing and spellbinding to understand how abstract looking mathematical concepts are applied in practical life.
Thanks and thanks ❤.
The best explanation ive everseen about sine and cosine. I gotta it at once. Watch again just to write down notes.
Awesome thank you so much!
I remember over 50 years ago we had books of tables sine & cosine, Logs & anti logs, no scientific calculators
Yes, logarithmic tables. It had important formulae of mathematics and physics. We were not allowed to carry them in the examination hall. If we had to use, the invigilators would give us copies of the log.
I am an engineer trained in the 60s and 70s. So I too remember the tables and the slide rule of course. Recently I tried to do a long division with pencil and paper and you know I couldn't remember how to do it! Took a while and some trial and error to relearn. Makes you really appreciate the power of a spreadsheets! Funnily enough using a slide rule's functions came back immediately and automatically last time I tried even after perhaps 40 years not touching one.
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We used both tables and calculators and it was amazing we were able to memorize so much of the tables by cross-referencing, this was in middle school
OMG, after watching many, and I mean many videos and textbook reading this is the absolute best resource I have come across. Wow, great job!!!!!! If you need Trig please watch this video. Its long but you will have a better understanding then anyone in the class. TRUST ME!!!!!
My teacher on internet.. big salute to you sir
Sir I really liked your "chopping" teaching method, Thank you I wish I had seen this 50 years ago!
Thank you so much!
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.
Me Too!
I think I can remember this now I will watch at least 1 more time. At 72 I found other ways around not knowing with help from many engineers (thanks to many) in my life. Your students don’t know how lucky they are to have you as a teacher! Mike
one of the best trig explanations on YT
Ok... I HAVE A QUESTION
I understand that HYPOTHENUSE is the WHOLE, the 100% if you will
I understand that the Cosine and Sine are a FRACTION of the Hypothenuse or more specifically A RATIO in both X direction and Y direction RELATIVE TO HYP
ok... so if X = 0.8 and Y =0.6
so... X means 80% of the force of THE HYP is in X
Y must therefore before 20% because hyp Is a representation of a whole
hence if it was a straight line it would be 1.0
How do we conclude that 80% + 60% = 100% ?
@NRG
you didn't answer my question
the question was...
How do we conclude that 80% + 60% = 100% ?
@NRG
oh.. i see
i interpreted it the wrong way.... my bad
You're dealing with a right triangle. So your equation *hypothenuse = x + y* ( from your *100% = 80% + 60%* ) is wrong. A hypothenuse is never the sum of the opposite and the adjacent. It has to be *hypothenuse² = x² + y²* as in the pythagorean theorem *c² = a² + b²* , so its *100² = 80² + 60²* or *1² = 0.8² + 0.6²*
@NRG When you walk 5meters on a hill slanted at 36.87°, you are horizontally 4 meters away from where you started going up and are 3 meters high from the ground. This diagonal movement doesn't mean you have walked 4 meters plus 3 meters. You WALKED UP 5 METERS at an angle of 36.87°.
In the same way, if you walk 100 meters on thay same hill slanted at 36.87°, you are horizontally 80 meters away from your departing point, and 60 meters vertically up.
You are thinking that the "total force" mentionned means literally the toral sum of two different numbers. What he implies by the "total" is, if that digonal line at an angle of 36.87 is 1unit (which is 1.00 o read 100 PERCENT) than the vertical line is 0.6 (which can be also read as 60%) and your horizontal line is always 0.8 (or 80%). Or put it differently, if your diagonal is a certain number, your vertical line is 60% of that number and the horizontal 80%.
I'm not usually good at explaining math but I hope this helped.
@@winxkorean
well... that certainly makes a lot more sense.
thanks
Is this free?! Sir, I would like to thank you for your presentation. You literally made it seem simple. I can't believe how much I learned about Trigonometry in only 48 minutes of your teaching. I know this is just the basic understanding of what you work with but your examples made a huge difference in the way I understand it. Thank you very much for taking the time to share this. I honestly wish there were more teachers/professors like you out there. I will be going over this again and look forward to more knowledge about the subject. As trivial as it is, an instant like and subscribed for me. Thank you.
Finally an instructor that speaks perfect English! Yea !!!
I bet algorithm has been biased to India 😂😂😂
I am 80 years and had a hard time with math .I will have to watch this a few times . Thank you. Wish I had you for a teacher when I was younger.
Simply put, a great great explanation. A great job. Thank you.
You're very welcome!
At foothill college, I had great teacher . Just as great as this man; God bless them!!!!
This lesson helps to explain why hip fractures occur mostly in women. Besides the osteoporosis, Femur hip angle is smaller in women, thus applying more force on the femoral neck. Thank you so much sir.
chopping function is really out of the box. Thank you sir.