09 - Unit Circle - Definition & Meaning - Sin(x), Cos(x), Tan(x), - Sine, Cosine & Tangent

[@zuffardi]

I'm from Argentina, Im 54 years old... and TODAY I UNDESTOOD SIN AND COS !!! THANKS

[@brandonmorad737]

Thank you very much, clear and accurate.

[@iainhenderson4222]

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.

[@mewsicman9541]

I rarely make a feedback on KZbin 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!

[@MathAndScience]

Thank you so much!!

[@TheByzmal]

Every other maths teacher is just reciting the syllabus. THIS IS THE ONLY PERSON WHO ACTUALLY TEACHCES.

[@JoeGator23]

I'm almost shocked by this man's capabilities to teach such an elusive subject. A+.

[@miguelaraujo1313]

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[@KHMERNATIONALIST]

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 .

[@andyramone8497]

100000% agreed.

[@carlllama6922]

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.

[@MathAndScience]

Love this. Thank you so much!

[@TheBackyardProfessor]

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.

[@atkapetr4064]

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 🙂🙂🙂

[@colinirvine757]

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.

[@kersi-sandiego6036]

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.

[@MathAndScience]

Hi Kersi - I really appreciate that - thank you so much!

[@deirdreberger1363]

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!

[@MathAndScience]

So true! Thanks so much for saying that! I really wanted to show where everything comes from rather than dumping it on the student.

[@Kaizen247]

Appreciated sir

[@SMAli78687]

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.

[@koangwiyuallliah6433]

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.

[@Matthewtriumph]

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.

[@Daniel-yt6ls]

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

[@xelaju8]

I am 51 years young and I am fascinated with all this new knowledge. Thank you for all these free lessons.

[@preethalal81]

I liked you say 51 years YOUNG

[@peanutbutter5463]

That is the best unit circle lesson I have ever had. Thank you.

[@oscarjrdepamaylo3673]

You really deserved more professor. I wouldn't mind watching a lot of ads as long a i hear from you ❤️

[@yinaxu2402]

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!

[@mariocesarsousa]

I really need it to learn Physics . Great teacher. Explains clearly

[@MathAndScience]

You can do it! Thank you so much!

[@lorenamacalanda9818]

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!!!!

[@arielbanzuela2277]

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.

[@MathAndScience]

Awww thank you so much!

[@muneerhussaindar]

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

[@theelectronicsengineeringg7362]

That was a very good way of teaching trigonometry, i loved it

[@MathAndScience]

Thank you!

[@seemazaman9360]

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.

[@carollockhart2546]

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.

[@shahrzadshamsafshar4286]

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

[@frankroper3274]

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!

[@beanhwak]

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.

[@bartkeelan1792]

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.

[@fromexoplanet21]

Hats off, you are the best teacher on the internet💖

[@CeMarie1024]

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!

[@raymondallenjhangiani7670]

Wonderful teacher ! The way you have explained everything in detail with amazing effort ? Sincerely appreciate the education you have shared ! God bless you always ! 🙏😇

[@yartelowusu3184]

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.

[@chriskundi5512]

Mr Jason, You are the most brightest Math Tutor I have ever seen I would like to meet you and learn more from you

[@lovernotfighter]

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.

[@MathAndScience]

Wow thank you!

[@mtaur100]

William Edmondson: I was just thinking the same thing. A good, effective teacher like this can make all the difference in the world.

[@freemind108]

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.

[@juliobaez9721]

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!

[@HVS2328]

I have a huge respect for you teacher. Thank you for clearing the fundamentals.💐🙏

[@KevinCook370]

I went to MTU for engineering....you have clearly explained these concepts...so excited to continue to re educate myself with your videos!

[@baraaktail6860]

The Best teacher!!!

[@MathAndScience]

I really appreciate the kind words!

[@MagicGenious]

@@MathAndScience yes I can also feel it

[@sanatghosh9278]

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.

[@manyande8682]

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 KZbin 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

[@ksatyasirisha2013]

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😂.

[@freemind108]

Wow a math hacker.

[@hugobusiness2741]

The world needs more of this. Thank you.

[@johnbertortega5086]

Sir thank you for your effort you will be an inspiration to coming new generation of scientist, engineer and teacher

[@MathAndScience]

It's my pleasure!

[@scophylio1]

It's the best lesson on the unit circle I've seen in years!

[@swapneshify]

u r beyond words.......i am now thinking why I was not ur student in my childhood, i am a bad luck guy.....after watching this video i am back to my childhood and now i am more interested in maths than ever .....Thanks a lot sir, "u r perhaps best among all".

[@caitlynashley5819]

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.

[@CapeAnneKayaker]

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!

[@Aerospaceman]

Makes more sense than it did 20 years ago. The lesson is excellent.

[@runoutarun5981]

you are doing good, no had taught me like you ! keep on going on your way ! we will support you !

[@minakumari9154]

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 ??

[@jaimevega3241]

I love this thank you! I finally get all this! You made math fun again. I'm hooked.

[@user-vv1do1wg1j]

Thanks man, one of the best teachers online i really cherish what you do tysm

[@MathAndScience]

I appreciate that!

[@1sweettime207]

Mr. Jeason you are a great and a humble teacher.

[@adityatyagi4009]

I wish my high school trig teacher had presented it the way you have. Absolutely amazing. Thank you so much.

[@nagyzoltan3973]

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

[@felixyongco4420]

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 ..

[@johnnybee1776]

Good teacher, excellent work You made it very understandable.

[@olivierbertin4255]

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

[@1978plankton]

Thank you so much for these videos! As a 41 year old going back to school. These are very helpful.

[@howieg2019]

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.

[@roniejabello5800]

I've watched many videos about unit circle but your video is the best, I easily understand it.

[@sisstm9813]

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!!!

[@glenwardgross366]

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!

[@natalysuelongares6252]

Thank you so much, sir! You're such a great teacher 😊

[@stwstw2814]

Hi

[@davidcarpenter542]

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 .

[@MathAndScience]

Thank you!

[@Amol-w2v]

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!

[@mstizzyfit2256]

You are so amazing!!! I am now able to help my daughter with her Pre-calculus

[@davidmadisontheguardian]

The denominator of all the middle numbers, 30, 45, and 60; all have a denominator of 2. Think of using the SIN first; and just count up for the numerator. 1, 2, 3; and reverse this order for the numerator of the COS. Only 4 numbers with respect to the quarter of the circle given; or within the 90 degrees have radical signs. And O and 1 switch places starting with 0 as the SIN. If you pay attention to the details; you see patterns; and putting patterns together helps you to get the full picture very quickly. Additionally, you change signs as in positive and negative as you go around the circle based on the quadrant that you're in. It may help to visualize rotating the same triangles around the circle in order to keep the relationships in your mind the same. Hope that helps.

[@rawdasamer2677]

thanks that is very helpful I would not know what to do without you your explanation is amazing

[@aerialrescuesolutions3277]

The Sin of 30 is 1/2 The Sin of 30 is 1/2 The Sin of 30 is 1/2...................... Love it, Jason , Awesome teacher..........

[@MathAndScience]

Lol that is awesome thank you so much! I bet you’ll never forget it!

[@aerialrescuesolutions3277]

@@MathAndScience I'm watching as many of your videos as I can now. I'm trying to figure out if I want a dvd set or a membership to access all the lessons? Any suggestions? Your big fan/student, James Rich.

[@MathAndScience]

Well it really comes down to personal preference. If you want to own the courses and have them on your computer to watch off-line and have them forever than purchasing is better. But there’s a great convenience to being able to login and stream all lessons at any time and you also have access to all the worksheets in the quizzes as well if you become a streaming member.

[@aerialrescuesolutions3277]

@@MathAndScience Thank you for the explanation. I sorta figured this was the case. I can take the dvd's with me anywhere. Streaming requires a computer and internet. All good. Jim Tree. Matrix,( Over and down, Over and down, Over and down).

[@RealMesaMike]

Yes, but if you do forget, you can work it out again by splitting an equilateral triangle with sides = 1 in half....

[@johnadriandodge]

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.

[@mohammadahmedragab837]

thank you so much, that is highly appreciated effort

[@michaelsalinas4329]

I'm preparing for a Physics and Maths Degree. I have never come across a more switched on lecturer A+++++.

[@manaka9778]

You have a clear explanation for lessons

[@MathAndScience]

Thank you!

[@MathAndScience]

Thank you!

[@ahmedmurad9703]

Super mathman I hop all lessons comes in KZbin for free You can tech the globe in the best way ever Thank you

[@vemburajm6189]

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.

[@zbigniewbrzezinski8869]

Thank you very much. Your lessons make it much easier to comprehend mathematics. May God bless you...

[@MathAndScience]

It's my pleasure!

[@AZ-vv1rf]

The first 10 minutes literally changed my life forever. I feel like I have just learned how to read.

[@MathAndScience]

LOVE hearing this!

[@mushtaqrasool9169]

The most underrated channel I have seen yet

[@manjitpalahe4129]

Requires extremes of patience in teaching and u r gifted

[@chelstonthomas1127]

I know you have heard it all before so, I will support you guys by purchasing the courses. You Sir are a treasure.

[@cozetplan8247]

Wow, you do great job of breaking math concepts down to the foundation.

[@MathAndScience]

Thank you!

[@wodeyaeric5351]

Ohhhhhhh Myyyyy God!!!! What a mathematics teacher this bro is!!! My first born is two years old. I wish u could teach her math and science when she grows up.

[@wodeyaeric5351]

So easy!!!

[@vascobishop3359]

Passionate teaching. A very good flowing lesson.

[@Mulavi]

Where were you forty-two years ago? Maybe it's taken this long for someone like you to come along to present these topics clearly. I'm curious who were the teachers that influenced your teaching style? You all deserve 👏🏼👏🏼👏🏼

[@davidmadisontheguardian]

I never went to college; other than a semester of Community College; and I've always wanted to learn calculus. I've decided after watching a lot of different videos from a lot of different channels; and then watching YOUR videos and then checking out your playlists page; that I will watch ALL of your videos. This could take me a year or more; but I feel the education I will get from everything you teach; will prepare me to be an inventor and to work with chemistry and physics. At the moment... I'm trying to understand why CHI can move objects. In order to do this; I'll need fundamental, CORE mathematics and science theory having to do with electromagnetics. I believe that after digesting all of your material; I will be well on my way to being able to propose my own theories with regard to CHI, Telekinesis or Psychokinesis or Mind over Matter; and the subject of the effect of the observer on the quantum model of the Universe. Like I said... it may take me a year or even two or three; but I plan on being proficient in these subjects in that time. Thanks so much! I liked every video that I've watched; and you now have a new subscriber. Wish more teachers/instructors/tutors were like you.

[@kulasekhararaogooty553]

Thank you so much Sir. I am a medical graduate from India and understood unit circle concept completely.

[@freemind108]

Its Just wow factor of visualizing trigonometry functions :). If one has patience of watching this video for atleast 10 minutes, one wouldn't downvote it for any reason.

[@godwinewulo681]

The video is helpful for the beginner. My son was sitting beside me, and he learned new thing on the current topic in his maths class. 7th Grade. Thank you.

[@adolfbotwey217]

I really find all your videos very educative. Thank you very much.

[@johannes.50]

You are the best teacher I never get bored of your lessons

[@thefinestsake1660]

You are my hero. I bet we are the same age, and I am just now getting this. Math teachers and profs before now just hammered sohcohtoa and told me to push the correct button on the calculator and not worry where it comes from. We never built the table or dissected the unit circle to understand how it all fits together . . . Or I might have fallen asleep. Anyway, I stayed awake for this one like a kid who just discovered how to count to 1million. Fantastic explanation of the fundamentals of the dark magic that is trig.

[@michaeldoyle4222]

Good work - Best video I have seen so far and the only video that includes the proof!!! Love it

[@ajsctech8249]

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

[@westsideproductions2695]

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.

[@jay22197]

Amazing.. Best teacher that I have ever had

[@thoughtpocket5189]

I enjoyed your honest about how little you end up using the unit circle even in pre-calc, but as someone studying calc 1 in college I can tell you I end up having to reference it often.

[@eddyboyblues]

wow.... never seen a awesome teacher like you.

[@ンサムハイ]

Thank you so much for this , may GOD bless you for your hard work ❤️.