Difficult subjects don't exists, but bad teachers do! Thanks for being one of the best. I like how you take your time and don't rush through the concepts.
I took quite a few math courses in college, but none of my instructors were as good as Professor Leonard in making the subject matter clear. I have to disagree with you though that difficult subjects don't exist. Difficult subjects exist even for the most brilliant people.
@@guitarista666 Whenever you find a subject too difficult, just remind yourself that it is developed by evolved monkeys! Thinking that a subject is difficult is actually a major set back when trying to learn it. If you have a good teacher and you spend enough time, you will see the footsteps of evolved monkeys in literally every subject.
@@matchmaticians5856 If everything is as easy as you describe, then why has theoretical physics hit a roadblock and has accomplished very little in the last 30 years? As far as understanding what someone else has done, that depends on your IQ. If your IQ is 85, you will not be exploring the frontiers of modern mathematics.
@@guitarista666 Yes, you can learn pretty much any subject with the help of a good teacher as long as you have the patience and you are willing to spend enough time on the subject.
@@matchmaticians5856 The US Army says that anyone who has an IQ of 83 or lower is too dumb to be taught how to perform any task that is useful to the Army. They have spent a lot of effort and money on this issue so we should take their conclusion seriously.. I know you're trying to be hopeful on this issue, but what you're saying flies in the face of the field of psychological testing. They say IQ matters and they can prove it. You should listen to them.
So I graduated with a BS in math a year ago. Professor L, you helped me all the way through. Im getting rusty and this was the first one of your lectures (in a diverse plan) that I know will help me back to my game. Thank you so very much. You are a wonderful instructor. Please keep up the great work.
Thought I 'd pop by to say thank you Prof. Leonard. It has been 9 years and you still at it. Your classes helped me a lot back then. I now got a career. Thanks. I wish you many more years and health to continue making a difference.
Öğrenciyim youtubeden gelir kazanmak istiyorum aileme yük olmamak için bu kadar insan içinde 100 kişi bile gelse bana cesaret vermek için yeter, şimdiden teşekkürler
18:10 - What were ancient mathematicians doing when they created the trig symbols: it would be symmetric and thus more intuitive in this pairwise: sine vs. cosine=sine^-1 (currently cosecant=sine^-1); secant vs. cosecant=secant^-1 (currently secant=cosine^-1); tangent vs. cotangent=tangent^-1 (current form).
@@ProfessorLeonard Hi Professor Leonard. Could you possibly do a video talking about the pre-Calculus concepts that we will need to do well in math in university? I want to go into engineering but I have a horrible foundation in math. Take care.
I consider Geometry a prerequisite for Trigonometry, since Trigonometry not only deals with triangles, but also with circles (the unit circle) and parallelograms (which are often used for finding lengths and angles).
@@user-qy6tu9ip9v where do I start? I guess the first one would be the numbers. Where do they come from? The answer to that is polynomials, Chebyshev Polynomials. So it's not just those numbers in the unit circle, there are infinite numbers and they all have polynomials associated with them. They start mixing in complex numbers at the seventh chebyshev polynomial. Those Chebyshev Polynomials have their own rabbit hole that involves pretty much every sequence in the OEIS database including Fibonacci/Lucas Polynomials. Which goes to Tribonacci Numbers and Polynomials. There is a Tribonacci Polynomial set that nobody even knows about. x, x^3+1, x^2*(x^3+2), x*(x^6+3*x^3+2), x^9+4*x^6+5*x^3+1 .. Then there is a unit ellipse with all the same polynomial stuff. Both of which are used in Mandelbrot Sets.
You are a WIZARD! thank you for these videos. My first day of trig class (its an expedited class) I was exceptionally lost! Lucky for me, my advisor suggested your videos and now I feel like im understanding better.
Professor Leonard, thank you for a tremendous lecture/video on explaining the Trigonometric Functions and the Unit Circle. These are probably the oldest topics in Trigonometry. These topics are also easy to understand from start to finish.
I started with youre precalc and I want to teach myself all the way to supersymmetry at home without college... please continue up to at least string theory... and then after that time travel then after that quantum field theory and simulation theory so we can fulfill our duty and make another simulation for the next generation to live... Stephen wolframmmmm and my dude nick Bostron... moment of silence for the Living Gods... archimedes, Hypatia, newton, Euclid and Professor Leonard... and many more
Öğrenciyim youtubeden gelir kazanmak istiyorum aileme yük olmamak için bu kadar insan içinde 100 kişi bile gelse bana cesaret vermek için yeter, şimdiden teşekkürler
He has Linear Algebra planned in the future, according to his information in the video "Professor Leonard's Important Announcement 2019". In the meantime, you could check out the book "Linear Algebra And Its Applications" by David Lay - that book is very good, and very easy to read.
Difficult subjects don't exists, but bad teachers do! Thanks for being one of the best. I like how you take your time and don't rush through the concepts.
I took quite a few math courses in college, but none of my instructors were as good as Professor
Leonard in making the subject matter clear. I have to disagree with you though that difficult subjects
don't exist. Difficult subjects exist even for the most brilliant people.
@@guitarista666 Whenever you find a subject too difficult, just remind yourself that it is developed by evolved monkeys! Thinking that a subject is difficult is actually a major set back when trying to learn it. If you have a good teacher and you spend enough time, you will see the footsteps of evolved monkeys in literally every subject.
@@matchmaticians5856 If everything is as easy as you describe, then why has theoretical physics hit a roadblock and has accomplished very little in the last 30 years? As far as understanding what someone else has done, that depends on your IQ. If your IQ is 85, you will not be exploring the frontiers of modern mathematics.
@@guitarista666 Yes, you can learn pretty much any subject with the help of a good teacher as long as you have the patience and you are willing to spend enough time on the subject.
@@matchmaticians5856 The US Army says that anyone who has an IQ of 83 or lower is too dumb to be taught how to perform any task that is useful to the Army. They have spent a lot of effort and money on this issue so we should take their conclusion seriously.. I know you're trying to be hopeful on this issue, but what you're saying flies in the face of the field of psychological testing. They say IQ matters and they can prove it. You should listen to them.
I attend UNT here in Denton, TX and you have completely saved my life with how you have broken down the unit circle. Thank you so much!
It is incredibly beautiful how logically you have laid out the relationship of these functions, where they come from, and why, wow!
College trig is the first math class to really stump me. These videos are the light at the end of the tunnel. Thank you so, so much.
So I graduated with a BS in math a year ago. Professor L, you helped me all the way through. Im getting rusty and this was the first one of your lectures (in a diverse plan) that I know will help me back to my game. Thank you so very much. You are a wonderful instructor. Please keep up the great work.
Nice hair cut. Also, I had a classmate tattoo this on his arm for reference in the class. No joke
Thats dedication, damn...
lol I might have to do the same thing
I wish I had professor Leonard at my university.
First time I found a new video the same dayThanks so much for your efforts in math education.
Another tough subject, explained clearly. Thank you!
you rewired my brain . Im a Turkish student and YOU changed my mine to math ❤
Thought I 'd pop by to say thank you Prof. Leonard. It has been 9 years and you still at it. Your classes helped me a lot back then. I now got a career. Thanks. I wish you many more years and health to continue making a difference.
why are you insulting him given he has helping a lot of students?
@@quant-prep2843 Huh?
?
@@roxynoz8245really HUH?!
@@user-fh2rw9zh8g I responded that way because your statement was more curious, indeed, less than true.
Hey professor leonard when can you expect this course to end?
Wish he did linear algebra because I'm lost in my class lmao
Hopefully that is next on his to-do list! He's covered all of the Calculus courses. Linear Algebra seems to be the next logical step.
Öğrenciyim youtubeden gelir kazanmak istiyorum aileme yük olmamak için bu kadar insan içinde 100 kişi bile gelse bana cesaret vermek için yeter, şimdiden teşekkürler
I'm late, but he covers linear Algebra in his Intermediate Algebra playlist, as well as helping to factorize equations. Hope this helps! :)
This poor guy can’t catch a break, it doesn’t matter what he does somebody wants him to be doing something else.
dude i forget all this crap really quick. This stuff is just dreadful
Great session Professor L!! Looking forward to the next vid! Thanks
Thank you. Professor Leonard.
Waaah. This is great. He really teaches so well.
Waiting for next videos on Trigonometry
Looking forward to the next video! Thank you so much.
Love you❤❤❤❤❤❤ from INDIA🇮🇳
my lovely prof , when are u gonna finish this course ???
18:10 - What were ancient mathematicians doing when they created the trig symbols: it would be symmetric and thus more intuitive in this pairwise: sine vs. cosine=sine^-1 (currently cosecant=sine^-1); secant vs. cosecant=secant^-1 (currently secant=cosine^-1); tangent vs. cotangent=tangent^-1 (current form).
Thank you 🔥🔥🔥🔥 you are the best❤️
Brilliant.....great teaching....loved it.
this is much easier to understand if you watch the video which follows this before this -N0. 7
Any chance of covering abstract algebra concepts
Sir maja(overwhelming) aa gaya
Awesome!!
What textbook do you use?
complete
Damn The Prof loss some muscle mass ¯\_(ツ)_/¯ Will always appreciate what your videos did for my finals
He says trigonometric, but the board says trigometric ...are both right/interchangeable?
Just an unfortunate typo. Sorry!
@@ProfessorLeonard Hi Professor Leonard. Could you possibly do a video talking about the pre-Calculus concepts that we will need to do well in math in university? I want to go into engineering but I have a horrible foundation in math. Take care.
I prefer Professor Leonard with a classroom audience. He feeds off the energy. Are we not going to get corny dad jokes now?
Corny joke at 17:40! I am so relieved and thankful. lol
I consider Geometry a prerequisite for Trigonometry, since Trigonometry not only deals with triangles, but also with circles (the unit circle) and parallelograms (which are often used for finding lengths and angles).
One way I practice is by using Khan Academy
The reciprocal of sine should be called secant, not cosecant. Likewise, the reciprocal of cosine should be called cosecant, not secant.
Secant and Cosecant have a complimentary relationship just as Sine and Cosine do. Hence the name.
You poor souls have no idea where this goes.
What do you mean by this
@@user-qy6tu9ip9v where do I start? I guess the first one would be the numbers. Where do they come from? The answer to that is polynomials, Chebyshev Polynomials. So it's not just those numbers in the unit circle, there are infinite numbers and they all have polynomials associated with them. They start mixing in complex numbers at the seventh chebyshev polynomial. Those Chebyshev Polynomials have their own rabbit hole that involves pretty much every sequence in the OEIS database including Fibonacci/Lucas Polynomials. Which goes to Tribonacci Numbers and Polynomials. There is a Tribonacci Polynomial set that nobody even knows about.
x, x^3+1, x^2*(x^3+2), x*(x^6+3*x^3+2), x^9+4*x^6+5*x^3+1 ..
Then there is a unit ellipse with all the same polynomial stuff. Both of which are used in Mandelbrot Sets.
@@thomasolson7447 Bruh.
The gifted current multivariably found because heat phenotypically undress as a fabulous cartoon. nice, strong multimedia
You are a WIZARD! thank you for these videos. My first day of trig class (its an expedited class) I was exceptionally lost! Lucky for me, my advisor suggested your videos and now I feel like im understanding better.
Professor Leonard, thank you for a tremendous lecture/video on explaining the Trigonometric Functions and the Unit Circle. These are probably the oldest topics in Trigonometry. These topics are also easy to understand from start to finish.
Just thought you should you should know that a gilette manly commercial played before this. Relevant advertising if I've ever seen it.
I started with youre precalc and I want to teach myself all the way to supersymmetry at home without college... please continue up to at least string theory... and then after that time travel then after that quantum field theory and simulation theory so we can fulfill our duty and make another simulation for the next generation to live... Stephen wolframmmmm and my dude nick Bostron... moment of silence for the Living Gods... archimedes, Hypatia, newton, Euclid and Professor Leonard... and many more
Can't wait for the next one! I'm really enjoying these lessons, thanks Professor Leonard :)
Thank professor. You are helping me a lot!
Öğrenciyim youtubeden gelir kazanmak istiyorum aileme yük olmamak için bu kadar insan içinde 100 kişi bile gelse bana cesaret vermek için yeter, şimdiden teşekkürler
There is no need to memorize the unit circle. It can all be done instantaneously with reference angles.
How can arc length be negative?
Si thanks I'm Indian ❤️❤️❤️❤️❤️❤️❤️
why do we multiply sqrt(3)/sqrt(3) to find the csc and cot? is it possible to leave the answer without multiplying?
cuz we always make the denominator to be numbers.
Please teach Linear Algebra. I have never felt so many gaps in my education without you teaching it. Please! Your viewers beg you!!!
He has Linear Algebra planned in the future, according to his information in the video "Professor Leonard's Important Announcement 2019".
In the meantime, you could check out the book "Linear Algebra And Its Applications" by David Lay - that book is very good, and very easy to read.
Aga be erimişsin be Leonard
Thanks Professor Leonard!
You did a great job 👍
Well now I just wonder why I'm here..
What textbook do you use for calculus?
I mean who's here to start learning lol
Great teaching sir
Thank you sir. Professor leonard
Can i get your lecturs in PDF file,please can u help me??
Just take your own notes when you are watching his videos....
@@fredavastine2922 thanks 🌹🌹
The return of the king