09 - Unit Circle - Definition & Meaning - Sin(x), Cos(x), Tan(x), - Sine, Cosine & Tangent
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- เผยแพร่เมื่อ 20 ก.ค. 2020
- More Lessons: www.MathAndScience.com
Twitter: / jasongibsonmath
In this lesson, we will learn what a unit circle is and why it is crucial to master in trigonometry, pre-calculus, and calculus. The unit circle is a circle of radius 1 (a unit radius) that is superimposed on to an xy plane. The points on the circle itself represent the sine and cosine values of the angles around the unit circle. In this lesson, we will spend our time finding the sine and cosine of the angles in quadrant one, and we will fill out a table of trigonometric functions at each of these angles. This is critical to master as understanding the first quadrant will help us find trig functions at any other angle around the unit circle.
I'm from Argentina, Im 54 years old... and TODAY I UNDESTOOD SIN AND COS !!! THANKS
Thank you very much, clear and accurate.
Every other maths teacher is just reciting the syllabus.
THIS IS THE ONLY PERSON WHO ACTUALLY TEACHCES.
I'm almost shocked by this man's capabilities to teach such an elusive subject. A+.
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I've learnt more about sines and cosines in the last couple of days than I learned in years at grammar school 50 years ago. Jason, you are a natural teacher and I commend you.
I have been in the wilderness of math for eons until Jason, the savior and shining light, appeared. A million to the 10th power thanks to you Jason.
Love this. Thank you so much!
That computer demo was absolutely PERFECT!!! I GET IT NOW!!!!!! You are awesome Jason! THANK YOU for such a fun and clear discussion! Oh how I wish I had this when I was in school all those years ago! But it is FANTASTIC to have it now also! I cannot emphasize enough how EXCELLENT your teaching is. Do MORE computer demos even up into Calculus if you can. That was SO VERY HELPFUL. I seriously cannot over emphasize that. I give you 10 stars out of a 5 star system! GRAND SLAM! I am thrilled out of my gourd to finally get the sin, cos idea.
Hi Mr mathematician
Your brilliant efforts have enlightened so many math students and math and science lovers .
I do appreciate your generosity for putting these lessons out , beyond comparison .
100000% agreed.
I rarely make a feedback on TH-cam lessons but this one is an exception. I am amazed at how you presented everything explicitly as you can, which most of my teachers failed to do. Your elucidated the concept way beyond my expectations. You've gained my respect! Thanks!
Thank you so much!!
Jason, your level of detail and commitment to the presenting of this information is truly outstanding. The care that you have shown is absolutely amazing. Congratulations on an outstanding presentation.
The critical important concept I understand clearly is that "Projection of Sine on Y-axis & Cosine is the projection on X-axis". Awesome explanation Sir.
Jason, you're the best teacher of Math I've ever met. You can talk about math as a great story of what mathematics truly is. I started watching your videos to help my son at high school. It honestly caught me, and now I study math every day. I wish you lots of happy students; you are fantastic. One of your happiest students, Atka, 56 years old 🙂🙂🙂
Outstanding teacher. I have many of his DVDs. Wish I had this guy in High School in 1959. Now his calc and engineering DVDs are great reviews for me of things long forgotten. This one on the Unit Circle is BETTER than his Unit Circle lesson on the pre-calc DVD that I purchased about 6 years ago. Thanks Jason for an excellent service.
Hi Kersi - I really appreciate that - thank you so much!
Jason you are the best teacher that I ever had in my life. I have been looking for this kind of teaching. Your teaching really make sense with the real world.
Huge congratulations! I'm really starting to love maths, physics and electronics thanks to you! Every day I choose a different subject to learn from your videos
Building it from scratch is so important! A lot of students are told to just memorize it! I wish all teachers would take the time to explain it like this. Excellent video!
So true! Thanks so much for saying that! I really wanted to show where everything comes from rather than dumping it on the student.
Appreciated sir
You really deserved more professor. I wouldn't mind watching a lot of ads as long a i hear from you ❤️
Thank u Jason ! you are selfless one and a rarity in this world. How I wish I had a teacher like you when I was then a young inquisitive student.
Awww thank you so much!
God has finally led me to something that transforms my trig. I spent my high school with out understanding what cosine and sine mean........you are really good at it be blessed.
Excellent teacher, I love the way he is explained the Sine and Cosine functions, super job! May God Bless you for making life of students easier.
That is the best unit circle lesson I have ever had. Thank you.
Dear Math & Science Teacher, I learnt so much from your video. Thank you so much for sharing the knowledge, being so patient by showing various aspects for us to understand and thank you, thank you!
I 've never listened so patiently to videos like this before, but u made me pay attention to details,, I salute you with your efforts Sir .. You did a GREAT JOB!!!!
You r the one who made me to understood it completely in my master's level.... And all trigonometric formulas i can understand now..
Thank u very much sir. Salute u
I am 51 years young and I am fascinated with all this new knowledge. Thank you for all these free lessons.
I liked you say 51 years YOUNG
Hats off, you are the best teacher on the internet💖
Where were you when I was doing this in college? I learned it all, but I would have got it all in one lesson with your instruction.
Wow thank you!
William Edmondson: I was just thinking the same thing. A good, effective teacher like this can make all the difference in the world.
Great, Thats Exactly the same question popped up in my mind. Its the teacher who can really make a difference in understanding the one concept to n-number of students at a time.
That was a very good way of teaching trigonometry, i loved it
Thank you!
You are amazing. You keep giving us these important helpful hints to be able to perform functions. Very rare in a Math teacher. They usually just keep spouting facts and functions without any explanation of why. You are very patient and thoughtful of what will help a student learn.
Wonderful teacher ! The way you have explained everything in detail with amazing effort ? Sincerely appreciate the education you have shared ! God bless you always ! 🙏😇
I really need it to learn Physics . Great teacher. Explains clearly
You can do it! Thank you so much!
I have a huge respect for you teacher. Thank you for clearing the fundamentals.💐🙏
I am 67 years old and am finally understanding what I was taught at school. Amazing tutoring. Would like to watch all your lessons on algebra, trigonometry and calculus.
If any one is having trouble memorizing sin angle values here's a trick. Remember this :- √(x/4). That's it. Now assume the angles 0,30,45,60,90 as 0,1,2,3,4 respectively. Now if you want sin 30, just replace x with 1(we assumed 30°=1) in √(x/4).
√(1/4)= √1/√4 =1/2. Hurray 🎉done.
Sin 45 = √(2/4) = √2/√4 = √2/2. And if you are thinking √(2/4)= √(1/2) =1/√2. You are absolutely right. And if you don't know (√2/2)=(1/√2), I don't know man, I don't know what to do😂.
Wow a math hacker.
I just love Jason! Jason gives you complete confidence when it comes to math! I've been subscribed to his channel for quite some time and Jason is such a blessing!
Mr Jason, You are the most brightest Math Tutor I have ever seen I would like to meet you and learn more from you
The world needs more of this. Thank you.
The Best teacher!!!
I really appreciate the kind words!
@@MathAndScience yes I can also feel it
The first 10 minutes literally changed my life forever. I feel like I have just learned how to read.
LOVE hearing this!
i remember almost 30 years ago in school, i couldn't learn this is my life depended on it, thanks to the many blessings of the internet, i at least got a clue now.
I wish my high school trig teacher had presented it the way you have. Absolutely amazing. Thank you so much.
thank you for your lesson I truly appreciate that a lot, I just can't thank you enough but I daily learn special content from you
I went to MTU for engineering....you have clearly explained these concepts...so excited to continue to re educate myself with your videos!
Passionate teaching. A very good flowing lesson.
I took the time to read some of the comments here and I totally agree! If you are cognizant and want to learn...this guy can make you a reasonably descent mathematician! This is the only channel on youtube I subscribe to!
It is worth attending, sir. you are the person, who can give crystal clear idea to student. I really prefer your teaching technique. thank you. sir.
Instructor Jason, Professor Jason, Dr. Jason, you are the most articulate and amazing individual I ever seen, and I have seen some very good ones. I am not in any of the fields you teach. I study your sessions as a brain stimulator. You have been blessed with a combination of tremendous talents. Thank You!
I love this thank you! I finally get all this! You made math fun again. I'm hooked.
you are doing good, no had taught me like you ! keep on going on your way ! we will support you !
You’re the best math teacher ever like dude you’re so good 🙂😄
My teacher just went over this lesson today and I didn’t get it that well until I finished watching this video!
I am a teacher by profession and I have not gotten better understanding of these Sin and Cosine thing practical than today. You made me love this rogue called Math and feel like learning more. THANK YOU.
Makes more sense than it did 20 years ago. The lesson is excellent.
Requires extremes of patience in teaching and u r gifted
Super mathman I hop all lessons comes in TH-cam for free
You can tech the globe in the best way ever
Thank you
Good work - Best video I have seen so far and the only video that includes the proof!!! Love it
Thank you very much for your teaching method. I am an Iranian, and after ten years I am trying to study in Iran, many important materials have been removed from all courses at this point in time, and everyone is forced to just memorize and not read the reason. But with the reason you taught me, I was able to understand completely. thank you so much
I really find all your videos very educative. Thank you very much.
I've watched many videos about unit circle but your video is the best, I easily understand it.
Took notes in notepad, so I had to abbreviate certain components.
Table of Trigonometric values:
sin = y or rise
cos = x or run
sin= y/r, cos = x/r
tan0 = sin0/cos0 = y/r / x/r = y/r * r/x = y/x = opp/adj or rise/run
t0 = sin0/cos0
cot = 1/tan
sec = 1/cos
csc = 1/sin
sr = square root
0 = angle
d = degree
I or U = Infinity or undefined = I or U
Important Sin30 = 1/2
outside of the unit circle resides coordinates which are depicted by cos(x), sin(y) x first, then y.
sin of 30 = 1/2, cos 1/2 = SR 3/2
Special numbers: 0,1,1/2/sr3/2,sr2/2
0 | Sin0 | Cos0 | Tan0 | Cot0 | Sec0 | Csc0
-------------------------------------------
0d | 0 | 1 | 0 | I | 1 | I
30d | 1/2 |sr3/2 |sr3/3 | sr3 |2sr3/3 | 2
45d | sr2/2 |sr2/2 | 1 | 1 | sr2 | sr2
60d | sr3/2 | 1/2 | sr3 | sr3/3 | 2 | 2sr3/3
90d | 1 | 0 | I | 0 | I | 1
There is no need to memorize this entire table but rather the six values of Sin and Cosine.
The hypotenuse of all of these triangles is one.
thank you so much, that is highly appreciated effort
Good teacher, excellent work You made it very understandable.
Your explanation is straight to the point, I respect it.
Mr. Jeason you are a great and a humble teacher.
Sir thank you for your effort you will be an inspiration to coming new generation of scientist, engineer and teacher
It's my pleasure!
The lesson is so perfect, I wish I had better words than thank you.
Thanks man, one of the best teachers online i really cherish what you do tysm
I appreciate that!
Thanks very much professor! You are the Epitome of teaching. Now I have a reason to understand what maths is all about. Now I have the determination to go back to college and finish it!!!
This guy is maths, why cant high school maths always be don't like this. Brilliant desire to teach maths and break down all the murky and unnecessary secrets. brilliant
I have always known that mathematics is an interesting subject but couldn’t just figure it out what to do in order to understand it. I have always wanted to do it up to advanced level despite not having a strong background so I decided to use TH-cam to search for videos that would make me understand it.
Your way of teaching has made me realize that it’s the way that most teachers teach that make people think maths is difficult.
I think it’s demonstration of application of what is being taught that will generate interest and curiosity in learners.
You sir have motivated me to go all the way and do mathematics. Can’t thank you enough
Sir did you write the number backwards on the outside of the circle at the 30 and 60? I have been using the PT since I was about 9 years old. My family was in the trades and PT was used all the time to what they call pull a square. 3,4,5 and 6,8,10 work great. I also learned the power of zero. I can add zeros to the numbers to infinity. As long as the numbers have the same number of zeros then the PT will always work. I hope this helps. BTW I am 60 years as of 2023/10/30 I have pulled squares for 51 years. Happy Birthday to any Marines that might be here. We love Triangulations. Send it!
I have no words to describe you but only one word for you. you are" Diamond". but where have you been when I really need your help while I was studying ??
thanks that is very helpful I would not know what to do without you
your explanation is amazing
You are so amazing!!! I am now able to help my daughter with her Pre-calculus
The most important property in the definitions of trigonometric ratios is the cyclic property The change from using right angle triangles in ancient math to using Cartesian coordinates make available the periodicity, a very important applications in our daily lives. We can represent all kinds of repetitive phenomena in waves and signals and not just build pyramids. Emphasis on the creative definitions using the Cartesian plane need to be greatly appreciated and recognized to give a big impact to the learner about mathematical innovations.
Now, after decades of struggling with these concepts, I am beginning to understand what sine and cosine are based on and what these numbers mean. Many thanks for the enlightenment! Now, my appetite for knowledge has really increased!
Thank you so much, sir! You're such a great teacher 😊
Hi
Talented and with huge energy!
Thanks Prof, you helped me to get it clear into the mind.
Hi Mr Math Teacher,
I have very much enjoyed this session of math in trigonometry. I have learned all this many years ago in a different language, however I want to express myself correctly, so I need to go through the lot in English again. Just like in clear communication your lesson ticks the 3 C's: Clear, Concise and Correct. I will watch all of your other videos as well, you are brilliant. Thank you, regards, Zoltán
Thank you so much for these videos! As a 41 year old going back to school. These are very helpful.
What a great professor.
Thank you so much cos I've learned so much from this video lesson.
Your explanations are so clear that my school teacher can't even provide.
What a great teacher. ! I wish I had had such a math teacher in High School
trigonometry. I struggled with this subject even in College .
Thank you!
Thank you, I needed to learn from the fundamental. Watch five times.
Absolutely brilliant! Love this lesson.
Excellent explanation! Thank you.
You are the best teacher I never get bored of your lessons
I was seriously about to smash my keyboard trying to do my online class because none of the instructional videos or textbook told you why or how to do any of the problems. You saved my life dude. Its all very clear now.
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Thank you!
I'm preparing for a Physics and Maths Degree. I have never come across a more switched on lecturer A+++++.
Thank you very much.
Your lessons make it much easier to comprehend mathematics.
May God bless you...
It's my pleasure!
Sir John , many of us in our time were confuse using the square root of 3 over 2 and the square root of 2 over 2 and 1 /2 VALUES.
The end result was to use the following VALUES .
1. The square root of 3 over 2 equals
0.866
2. And the square root of 2 over 2 equals 0.707
3. And the sine of 30 which is 1 /2 we used instead 0.5
4. The end result : Our answers must be correct to 2 decimal places.
5. Finally all were adjustef later to 1 / 2 and squre root of 3 over 2. and tge square root of 2 over 2. and learn the X AND Y - COORDINATES ( X , Y ) VALUES..
6. All were happy in the end to. later understand the ARC SINE , ARC TAN , ARC COS .. ETC..
THANK YOU VERY MUCH SIR JOHN IN CLARRIFYING OUR. CONFUSED STATE MIND.. YOU ARE THE GOD SENT.. TO EDUCATE US.. BETTER ..
YOU ARE ONE IN AMILLION . THE BEST.. I AM STILL LEARNING AND MORE.. AND MORE..AND MORE ..
Great presentation!
Amazing.. Best teacher that I have ever had
The most underrated channel I have seen yet
I must thank you for this lesson 💐
Your videos are awesome. I could find only the old videos of Trig and Precalc in playlists. If you could make these new videos as a playlist it will be helpful.
Thank you for your efforts.
Thank you so much for this , may GOD bless you for your hard work ❤️.
This great, thanks again. Think I might just watch the whole playlist.
I know you have heard it all before so, I will support you guys by purchasing the courses. You Sir are a treasure.
Too good. I can not say more than you are the best and proficient educator.
How I wish you were my. teacher in my. first year of electrical studies
58 or so years ago.
We do need to memorize the SIX TRIGINOMETRIC FUNCTIONS ..and our EXAMS twisted our. brains using the. INVERSE FUNCTION type of QUESTIONS.
EXAMPLE :
CO TAN THETA
CO SEC THETA
HEAVEN KNOWS. ..KIDS ..LIKE ME BECAME. SILLY IN THE END.. TO ARRIVE A CORRECT ANSWER . INCLUDING SIGNS IN THE SECOND , THIRD AND FIURTH QUADRANT OF THE UNIT CIRCLE.
SIR , THANK YOU SO MUCH GIVING US ENIGHTMENT
MATH AND SCIENCE LESSON.
AND MORE TO COME....
wow.... never seen a awesome teacher like you.
You make math alive!, top.
That teacher right there is indeed not a lazy ninjah. I like to be bigger than the master. Amen
The computer demo was very helpful. Thanks for including that!
You are very welcome!