Sir, you are a legend and hero in the eyes of every student who watched your video after spending years living in fear of the trig and the unit circle.
when teachers say memorize this it is so annoying, because ideally you should memorize very little; everything else should follow naturally from what little you did memorize
Memorize is a misnomer. Your goal is to "Internalize". Its not about rote memorization at all. You don't tell someone to memorize how to ride a bicycle. Rather you teach them how riding a bicycle works. Then let them do it until they *understand* what they're doing. Afterwards they will know how to ride a bicycle till they die.
Here are a couple of thoughts: understanding and memorization are not the antithesis of each other! There is no understanding without memorization, although there is often memorization without understanding! Second “very little” is a relative term. All of the flash cards that he displays are just things that have NOT yet been stored in long-term memory! Thus far, I’m about 75% through this video and there have been SEVERAL flash cards and a couple of mnemonics (SOHCAHTOA, e.g.)! While you may say these required “very little” memorization, I think they are not so little! Understanding is the ultimate goal, but it will NEVER occur without significant investment in memory! I get your overall point and the message of this video: memorization without understanding is pointless! But understanding without memorization is futile!
I've been teaching mathematics for 32 years. This is simply the best introduction to Trig I've ever seen. I did not hesitate to share this with my Precalculus students. Thank you.
I am 44 years old but I can't understand the trigonometry clearly during my school time and unfortunately I blamed the mathematician who invented it. I am very grateful to you for a clear understanding. Again Thank you Sir.🇮🇳
This man has confirmed my belief that if you are telling your students to memorize concepts, you do not understand them yourself and should not be teaching them.
What are the flash cards for? What’s the MNEMONIC SOHCAHTOA for? Believe it or not, there is a reason that we have long-term memory! Understanding begins with memory!
NEVER in my life (and I am 75) have the fundamentals of trigonometry be shown to me in such a clear manner. Thank you so much ! Greetings from Belgium, Patrick WOUTERS.
After 3 separate trig classes, this is the first time I've actually intuitively understood how the unit circle works, and haven't needed to memorize things to get through tests and assignments. I wish all math teachers would teach as clearly and concisely as you do.
I've always been a visual learner and failed in school due to being told to memorize, but without reason my mind would not lock it in. This video was extremely useful, massive thanks.
"I'll never use this in my lifetime, so why do I need it?" Me, in 1986. Fast forward to 2008, used the 3,4,5 method to check a wall to see if it was square. I think I saw it on This Old House, lol. Use it all the time now. I use angles every day as a carpenter. I try to keep learning, so in the mornings, I watch how-to videos. I love math. I love the look and design of the math equations and every day I learn something. Thank you for the visuals. That is a huge help.
As a carpenter I used the 3,4,5 for nearly 8 years till an electrician friend taught me the Pythagorean Theorem. That opened up a lot for me, but when I started learning this trig stuff on youtube I really felt like a fool. My teachers were so bad in school, I never got past pre-algebra. Anyway here is link to a 8 minute video I thing you would enjoy. ua-cam.com/video/Dsf6ADwJ66E/v-deo.html I found it in the comment section.
@@simpleman283 That video is pure poetry. Wow!! Amazing. My schooling was the same, but I always loved math and physics. There is a mystery there and I'd love to figure it out. lol if that makes any sense.
I took trig my first semester in college. Six years later, I went back to college to finish up. In my Calculus class, they ran a quick quiz the first day. It said I had a 30% chance of passing. A friend came over for supper that night and he drew out this information for me. I posted it above my work desk. It made all the difference! I very nearly got an A that semester in Calc 1. Visualization and memorization can work together to make you a master of this information.
Mr Davis I’m a medical doctor, which always been interested in mathematics physics calculus and such, my late father was an engineer maybe that is why I’m interested in this. For what I remember when I was in high school I was never been explained this concepts as you are doing here, now I’m hooked to this Trig series as a high school kid It’s always fantastic to learn something new, but it’s even better to perfectly understand the concepts the way you explain them Thanks a lot!!! Wish we had internet and UA-cam when I was a kid
Dennis, I'm 62 and this was my introduction to trigonometry. I failed algebra 1-2 and never made it to trig or calc. I grew up in a family of engineers. I used your pattern technique to memorize my multiplication tables. Couldn't remember the individual combinations of numbers but I could round things to fives and tens, extremely quickly. Your cheat isn't original but you're the first person I've ever met that taught math that way, Thank you. I went into the field of horticulture, plants. Landscaping, particularly the Japanese garden, fascinated me. It is a universally loved form of art in my field. Geometry is my native mathematical language in my head, All I see is patterns. Turns out the Japanese Gardens magic is tied up in endless triangles. Once you can visually dissect the design all you can see is the triangles. Somehow they figured out how to landscape in trigonometry. Countless acquaintances have told me I would have loved trigonometry. I would have. Thank you for tying a lifetime of interest together into one handy bow. Mark Barton
It's incredibly easy. I don't know what about it trips people up. It's literally memorizing formulas and algebraic manipulations of said formulas.@@rpruneau68
FLASH CARD/CHARTS/FORMULAS TIME STAMPS 5:43 trig functions (SOHCAHTOA) 7:39 trig functions (reciprocals) 11:18 quadrants (Cartesian Plane) 14:49 chart (Radians) 20:13 formula (Pythagorean Theorem) 24:42 3 numbers (Unit Circle) I saved your trigonometry course and I will try to finish it. Despite some of the math I will study would not be use in my daily life someday. I still would love to be enlighten and enjoy learning with it.
Best trigonometry class that I have ever sat in, man, we were never taught like this at all, it's like our teachers never wanted us to understand this concept or maybe they never understood it themselves in the first place so we're doomed. Long live Sir Davis.😊😊
this might be embarrassing to say, but I'm in my first year of college/uni and this is the FIRST time in my life that I have ever understood trig! It's one thing to know math, and another one to teach it, and you sir, know how to TEACH!!
First time - I understand this on a visual matter. Instead of learning formules without knowing what I was learning. I agree with another respons that you should have 1M views for this YT video.
Just a stunningly great tutorial. So many kids in 99% of high school literally quit school, because poorly taught math courses like Trig rips their soul. This should have 1 billion views. Your video should be a pre-requisite for ALL middle and high school math teachers, and ALL Freshmen college students. Seriously!!
You, Mr Davis, Sir, are an absolute genius! You are able to teach a not-so-easy and intimidating concept to make is as easy reading a road map by using its legends!! I'll gladly pay to join your Trigonometry classes (probably other math classes, too). Thank you, thank and thank you again!!
@@DennisDavisEdu You have what many instructors lack which is the ability to teach knowledge to others. Thanks for sharing, but I would purchase a course from you.
after years of my life spent not understanding trig, this video finally made it click. i’m a visual learner and have a hard time with math because of this, but your teaching style makes it so much simpler to understand! THANK YOU!
I'm a visual learner too Paisley. I'm creating videos I wish I could have seen when I was in school. I often thought "If only someone would have explained it this way I would have understood much better!" So that's what I'm trying to do! I'm glad you found it useful. I've just posted a full trig course that goes into more detail and follows the same graphical teaching style. Happy learning!
@DennisDavisEdu I can not express how much I appreciate this, I am gonna enter high school next year and have been dreading trignometry since 4th grade, but now with your course, I can complete it ahead of time! You are helping millions of people learn, keep up the good work, and thankyou for your contribution to humanity❤
THIS. IS. BEAUTIFUL!!! The applied mathematics approach is the only real way for many of us to learn. These basic foundations really help improve my CMM and GD&T knowledge. I'm SO happy to have found this series and cannot wait to jump into the Statistics course before taking my Six Sigma exam. Thank you so much for taking your time to do this and I hope that your channel grows so that we have more resources like this! You and TheOrganicChemistyTutor are changing the game!
@@DennisDavisEdu I must say so too, I'm impressed and very thankful. Just started 10th, and very afraid of trigonometry, and u cleared the whole chapter for me before my teachers even got to try. Even if they do, they would just drag on the chapter for 2 weeks where all the students would be told to memorize everything, but in just half an hour, you cleared the whole chapter without telling me to memorize anything, u definitely earned a subscriber
This deserves millions of views. My teachers told me to cram T-raios without explaining what they actually are, and that's where this becomes annoying. Thank you very much for providing such a great video learning by visualisation and understanding can make anything easier.
I’m just letting you guys know that I’m not even in school for anything, I’m watching this because it’s available and that’s what I find wonderful. This person for free made this and has probably warranted someone a career that pays them 100k$+.
Excellent presentation. I never had Geometry and was homeschooled and now I'm in college trig. This tutorial is a lifesaver and better now than never although I wish I'd seen it 2 weeks ago before class started. Appreciate you creating this content and look forward to watching your other vids.
I've been out of high school for 19 years, and I stumbled upon this video. I am still absolutely blown away by mathematics and the relations of numbers to each other. Thank you for this lesson.
Hey Dennis - Where were you 55 years ago, when instruction like this would've changed my life! I am so jealous of the Kids these days with their access to Instructors like you and the clarity of that instruction. Now I'm using this to catch up, review and explore so many new and exiting fields of interest. Thank you so much.
Thank you Mark for those kind words. It's never too late to learn something new! I agree with you: Today anybody can learn anything they want for free. Not at all like when we were kids.
I swear my teachers just show how to solve problems, NOT how to understand them, and understanding is the basis of higher maths. Thank you so much for this video. It helped alot and is an incredible source of knowledge and understanding.
Learnt this area of mathematics 50 years ago. The teachers then did not introduce the subject in the way you have done. They just started off with the definitions and jumped into problem solving. Such method was a nightmare to students. Your way is simple and lucid.
Daniel, I wish I could take this video back in time 20 years. You made me understand what took me over 24 months back in high school to memorize so I could pass an exam, and you did it in five minutes.
Sir you are amazing. You have demystified trigonometry in 30 mins. I must say that I am now in love with trigonometry. Sine, cos and tan have now their own personalities. They are tangible and very much useable. I wish calculus and imaginay numbers could also be conceived like this.
I'm nearly done with my math degree and I've been using trigonometric functions and the unit circle literally everyday for years. I came here to learn the basics so I can use trig identites, differentials, and integrals without memorizing. This is such a good foundation. thank you
You have no idea how much you have helped me. I'm taking a fast paced TRIG class in college and haven't done trig since junior year in HS and was completely lost until this. The course is suppose to cover all of trig in 5 weeks :/
I'm 50 years old and I back in high school, I had to repeat Algebra so, I never had trigonometry. I really wish I did because I think this is a fascinating subject. Good thing for UA-cam and videos like this made by someone who knows and can explain the subject, to make it possible. Great video!!
Before I watch this, I've never taken a trigonometry course before. I was a year ahead in getting to Algebra in grade school but even now in college, I'm still only advanced as far as Algebra w/ Communications, which from what I can tell is essentially "College Math For Idiots: The Class". And the problem absolutely is visualization. In my sophomore year of high school, my geometry teacher was also my soccer coach, and he would use soccer to visualize math in class and basic math to conceptualize soccer and drill formulas in practice. He was without a doubt my favorite teacher in all of school who wasn't also teaching music. (If you happen to watch this video Coach May, Hi!) But he was my only math teacher after my 8th-grade year bothered with it before my current math course. Algebra 1 and 2 I just couldn't grasp them conceptually because drilling formulas is ALL that so many public schools do. Why do the numbers act the way they do? How do all of these letters relate to each other? Why is Coach May the only one who seems to be able to tell me what y=mx+b MEANS when it's the formula for a slope? Because eff you, read the formula again and follow the steps, that's why. Only now that I'm in college I seem to be finally grasping Algebra on a conceptual level because my Professor actually drills problems in class, and writes EVERYTHING on the board to connect every term in the problem. I'm still having some trouble actually following the steps in the right order to get the right solution, but tutors have been a good reinforcement, and I'm genuinely starting to improve. UA-cam videos about math make it engaging and fun for once in a way I haven't felt since I was making multiplication tables. I'm finally starting to see how engaging math can be again, and the fact that the wonders of math stop being explained conceptually after you're finished learning basic arithmetic in public school ought to low-key be criminal. So thank you. As I prepare to watch this video as my very first exposure to real trig, I know I'm not going to understand all of this for probably a long time. But I'm confident by the sentiment of the title alone that what I'm about to see will be engaging, and further spark this newly found passion, even if passion hasn't yet translated into skill on my part.
That's a nice story, thanks for sharing. I agree visualization is the key to deep understanding. Now I'm afraid this short overview will disappoint you because it is not a deep, thorough introduction. It just scratches the surface visually. For better, deeper trig coverage, please see my multi-part playlist linked in the description. Happy learning!
You have my respect! I am 70 years old and I wish my math teacher had shown your methods, we were always being told to memorise, memorise, memorise! Can’t beat a little brain exercise!!!! Thank you very much!
This is the first time I’m commenting on a UA-cam lecture video and that’s cos I’m beyond wowed. This is hands down the best lecture I’ve had in my life. Thank you! 🙏🏽
Wow. I thought I was the best teacher when it came to introducing the ideas of trig so as to not be intimidating, seem like common sense, and easy to remember (by simply figuring out.) After 30 years of this, I take off my hat, and bow to the man who has bested me.
I’m an English as a second language teacher. I love these memory hacks. It helps to give first time learners edge of confidence that they could learn further. Truly the heart of a teacher.
You just save me a ton of time for studying!! i am a "figure out" person, i cant just "memorize" things and take them as "face value" there must be a REASON for them, and you just prove it!! Thanks!!!!
Thank you! This video is incredible. Not only it demystified trigonometry but now I actually understand. Like someone else mentioned, this is "Gold Standard" teaching.
11:35 imo, this would have been a good spot to shoehorn the "right hand rule" in as a memory aid for the direction that the angle sweeps positive as that is also a very fundamental concept much later. "Just point your right thumb at yourself and notice the direction your fingers curl". This will also address any potential ingrained mental bias towards clockwise motion.
I never understood the conversion of degrees to radians intuitively, and now I’m a master at it. As corny as it is, you did what my math teachers could not. Thank you so much.
Watching this video solidifies in my mind, just how much time was wasted going to school. I was stuck in Trig for 4 years, never understood it as well as I have now in this short 30 minute video. I appreciate what you're doing to help accelerate our up-and-coming generation. I just hope it isn't too late.
Sir, im father aged 45 of a boy from India who is in grade 10 and i amazed if i could see it when i was in his age. My son finds it helpfull too. Hat's off to u sir.
Best video ever. Sir, you're an absolute legend. I'll rewatch this video many times from now on. I could understand in two days a topic that I was so afraid of for months. I'm actually in precalculus and I this has saved my life. Thank you, sir. I'll watch your other content and subscribe! Hope you continue being a math hero! 👏🙌
Thank you Manuel for your kind words. I think my big Trig series (see description for link) is so much better than this video, but this one gets all the views and nice comments. That series has 80 videos right now, but every day this long-form overview video gets more views than those 80 combined. Well, the customer is always right! Thanks again, I'm glad you were able to overcome your fears. A little knowledge can give confidence, and confidence fights away the fear!
I always did trigonometry just by memorizing but at the same time did wonder what actually they are and how should I visualise them, but after watching your video, my years of questioning myself has finally come to an end. Thank you so much.
My new trig series has been posted... ua-cam.com/video/NBC4ZvCt2Lg/v-deo.html It is a series of 46 mini-lectures with (I think) improved style and clarity. It is more in-depth than this simple overview. Dennis
The series won't be completed for some time, but it is much more in-depth. This one covers the essentials, but I had to leave some stuff out, like the most famous equation in trig: cos²θ +sin²θ = 1. For quick overview, stay here, for more in-depth, see the series. Or watch 'em all!
Check out my longer trig series linked in the description. It's more of a full semester's worth of information taught in the same style. This video is just a high level overview. It sounds like your daughter is in good hands. Best wishes to you both!
AI engineering student: Thank you for breaking that down in simplest terms- you've made a significant improvement in my comprehension of the unit circle and what exactly the trig functions are and what they mean. I truly appreciate this knowledge- it definitely beats trying to memorize like a fool. I crave to comprehend always.
Thank you so much for this. 13:14 I never was taught that, instead I was taught to remember some formula on how to convert form rad to degrees but never got an explanation why
I was about to rip off my maths books and throw them away after how I suffered but sir you LITERALLY SAVED ME WHOLE LIFE THANKS ALOT this is the best trigonometry lesson I have ever leaned
There's not as much to memorize in trig as you might think. If you understand the concepts, you can figure out most things quickly and with less stress than memorizing. And you enhance your understanding!
the last part with the small, medium, large is a big help. That is really easy to remember and use. I was struggling with trig when they appear on graphing problem in class, now I feel like I can solve them on my own. Thank you very much!
Oh my God! I hadn't expected this video to happen. It has helped me with a mountain of exercises since I was in 12 grade, a junior high school, I had learned Physics in general, and trigonometry in particular. At that time, I was stuck by the death circle, 'cause I couldn't remember the numbers well. But when I watched Dennis Davis's video, I completely changed my mindset to the Trig. It's easier to have a deep understanding, and, of course, Davis I'm now always visualizing not memorizing as you said! Anyway, Thank you so much for making an incredible video!
I was only taught the sin, cos and tangent. While I knew about the other three, I was never introduced to or used them. Thank you for a most informative class!
Me too, and happy with it. Why introduce yet another function name for say 1/sin(x)? For me sin, cos and tan, their series expansions, the complex exponential and Euler's identity are all trig I bother to remember.
fourth year math undergraduate, worked with discrete math for a while but taking an interest in analytic geometry and this was the perfect reintroduction to trigonometry, thank you!!
This video on trigonometry turned out to be the most understandable and informative of all that I have seen before. I did not even notice how 30 minutes of the lesson had passed, while I was absorbing the information with interest
Good sir you are a blessing I've been avoiding trigonometry for more than a year because of the unit circle, but you taught it to me so easily i can not sufficiently express my gratitude to you good sir THANK YOU VERY MUCH
Stumbled into this one was was blown away. Out Standing Troop. Beautifully elegant and simple. Yes boil it down. The graphics were great. Cutting board great. Help set the perspective with the origin. Brings back do much. Today retired but gmdijnv CAD for 3D printing parts for my 1950s model train. Still beef to know angles and ratios but oh My God so long ago. This was an awesome refresh. Thank you. Dennis
excellent! these are the same sorts of tricks I came up with to avoid memorizing things too. It's not laziness, it's about being practical. I recognized in high School that I would never remember everything forever, and that the less I had to memorize, the more likely I would remember it long term, and focused instead on being able to use those basic core concepts to recreate or solve for anything else I needed later on. I didn't learn the concept of "first principles" until well over a decade later in life, but that's basically what we came up with.
Early childhood education needs to be flooded with these kinda teachers.. the world will be a better place 🙂, A nation of thinkers given such a stepping stone breeds better scientists
If you want to be good at calculus, you have to be good at trig because it is the foundation for understanding concepts of basic calculus, advanced calculus, linear algebra and physics
No, knowledge of trigonometry is not needed to understand calculus. In calculus you will perform "operations" on functions. (The operations are called differentiation and integration). You'll probably start out with linear and polynomial functions because they're the easiest to understand the calculus "operations". But eventually you'll get to functions that include trig functions in them. You don't need to be a trig expert to do this, and trig is certainly not a foundational requirement to learn calculus. When you get to the trig functions, it would probably be helpful to see the graphs of the trig function in your head or be able to sketch them out quickly. See video TR-18 in my more detailed trig series here: ua-cam.com/video/f99P31SAsek/v-deo.html
outstanding sir i was very much stuck at sea without a paddle and now i feel like i was over thinking most of it. one of the best maths videos i have come across. Thank you.
I was an extremely good math student in high school. Won math tests and stuff... not braggin'... maybe braggin' a little. Anyway, I took calculus 2 in high school, but there was only one class that ever really frustrated me... trig. Trig was the first class that felt like memorization and math to me has always been about conceptualization... not memorization. Anyway, I had to develop the conceptual tools myself, and it was the hardest math class ever for me... I wish I'd seen this video when I was taking trig. My advice to anyone... watch this video enough times that you understand every single word. If you can wrap your brain around this video, you will be able to pass an end of course trig exam. You will only need a few more conceptual tools and memorized formulas to ace it. This video is enough framework to get you most of the way through the course. Fantastic job Mr Davis. Don't take this video down. When my kids are old enough, they WILL be watching this video.
I’m an IT student and It’s too late that I’ve just discovered your channel. Now I go back here to get a refresher about the unit circle because of Calculus. This is way too easy to understand. Why did I come here late😢 In just a few minutes, I easily memorized how you delivered everything😢 too late…
Sir, you are a legend and hero in the eyes of every student who watched your video after spending years living in fear of the trig and the unit circle.
What a nice thing to say! I'm glad you found it helpful.
Absolutely!
@@DennisDavisEdu Really precious scenes♥️
@@DennisDavisEdu Now if only someone can teach these young WOKE fools that only two genders exist, and that thinking otherwise means you're an idiot.
ONG 😤
when teachers say memorize this it is so annoying, because ideally you should memorize very little; everything else should follow naturally from what little you did memorize
Memorize is a misnomer. Your goal is to "Internalize". Its not about rote memorization at all.
You don't tell someone to memorize how to ride a bicycle. Rather you teach them how riding a bicycle works. Then let them do it until they *understand* what they're doing. Afterwards they will know how to ride a bicycle till they die.
Here are a couple of thoughts: understanding and memorization are not the antithesis of each other! There is no understanding without memorization, although there is often memorization without understanding! Second “very little” is a relative term. All of the flash cards that he displays are just things that have NOT yet been stored in long-term memory! Thus far, I’m about 75% through this video and there have been SEVERAL flash cards and a couple of mnemonics (SOHCAHTOA, e.g.)! While you may say these required “very little” memorization, I think they are not so little! Understanding is the ultimate goal, but it will NEVER occur without significant investment in memory! I get your overall point and the message of this video: memorization without understanding is pointless! But understanding without memorization is futile!
I agree! math is not about memorising. It’s about understanding and applying.
totally agree, math is understanding not just memorize, this is math, not history
Thanks 👍
I've been teaching mathematics for 32 years. This is simply the best introduction to Trig I've ever seen. I did not hesitate to share this with my Precalculus students. Thank you.
I needed to read this; I'm about to take pre calc in college and I wasn't sure if this will be part of the class.
Indeed you are one in a million 🙂
Not alone
Tbh I'm on calc now and still needed this @@rul1175
I am 44 years old but I can't understand the trigonometry clearly during my school time and unfortunately I blamed the mathematician who invented it. I am very grateful to you for a clear understanding. Again Thank you Sir.🇮🇳
This man has confirmed my belief that if you are telling your students to memorize concepts, you do not understand them yourself and should not be teaching them.
Agreed
in psychology this is called confirmation bias :) glad I could help.
What are the flash cards for? What’s the MNEMONIC SOHCAHTOA for? Believe it or not, there is a reason that we have long-term memory! Understanding begins with memory!
@@hc3550idiotic child
NEVER in my life (and I am 75) have the fundamentals of trigonometry be shown to me in such a clear manner.
Thank you so much !
Greetings from Belgium, Patrick WOUTERS.
same here
And yet you made it to 75 just fine without seeing it in a clear manner.
i said the same thing
@@ExtrovertedCenobite yah but imagine had he learned this in his teens he could have conquered the world!
@@tedpatriot2963 I know of many who have mastered many fields and have not conquered the world.
After 3 separate trig classes, this is the first time I've actually intuitively understood how the unit circle works, and haven't needed to memorize things to get through tests and assignments. I wish all math teachers would teach as clearly and concisely as you do.
90% are incompetent
Only if they themselves knew what they are teaching. Many are teaching from rot memory.
I've always been a visual learner and failed in school due to being told to memorize, but without reason my mind would not lock it in. This video was extremely useful, massive thanks.
"I'll never use this in my lifetime, so why do I need it?" Me, in 1986. Fast forward to 2008, used the 3,4,5 method to check a wall to see if it was square. I think I saw it on This Old House, lol. Use it all the time now. I use angles every day as a carpenter. I try to keep learning, so in the mornings, I watch how-to videos. I love math. I love the look and design of the math equations and every day I learn something. Thank you for the visuals. That is a huge help.
As a carpenter I used the 3,4,5 for nearly 8 years till an electrician friend taught me the Pythagorean Theorem. That opened up a lot for me, but when I started learning this trig stuff on youtube I really felt like a fool. My teachers were so bad in school, I never got past pre-algebra. Anyway here is link to a 8 minute video I thing you would enjoy. ua-cam.com/video/Dsf6ADwJ66E/v-deo.html
I found it in the comment section.
@@simpleman283 That video is pure poetry. Wow!! Amazing.
My schooling was the same, but I always loved math and physics. There is a mystery there and I'd love to figure it out. lol if that makes any sense.
I said the same thing . Now use it all the time in pipe fitting
I took trig my first semester in college. Six years later, I went back to college to finish up. In my Calculus class, they ran a quick quiz the first day. It said I had a 30% chance of passing. A friend came over for supper that night and he drew out this information for me. I posted it above my work desk. It made all the difference! I very nearly got an A that semester in Calc 1. Visualization and memorization can work together to make you a master of this information.
Mr Davis
I’m a medical doctor, which always been interested in mathematics physics calculus and such, my late father was an engineer maybe that is why I’m interested in this.
For what I remember when I was in high school I was never been explained this concepts as you are doing here, now I’m hooked to this Trig series as a high school kid
It’s always fantastic to learn something new, but it’s even better to perfectly understand the concepts the way you explain them
Thanks a lot!!!
Wish we had internet and UA-cam when I was a kid
omg, so this is what they mean that math is easy as long as you really understand it. every explanation has explanation holyshit feels good
Dennis, I'm 62 and this was my introduction to trigonometry. I failed algebra 1-2 and never made it to trig or calc. I grew up in a family of engineers. I used your pattern technique to memorize my multiplication tables. Couldn't remember the individual combinations of numbers but I could round things to fives and tens, extremely quickly. Your cheat isn't original but you're the first person I've ever met that taught math that way, Thank you.
I went into the field of horticulture, plants. Landscaping, particularly the Japanese garden, fascinated me. It is a universally loved form of art in my field. Geometry is my native mathematical language in my head, All I see is patterns. Turns out the Japanese Gardens magic is tied up in endless triangles. Once you can visually dissect the design all you can see is the triangles. Somehow they figured out how to landscape in trigonometry. Countless acquaintances have told me I would have loved trigonometry. I would have. Thank you for tying a lifetime of interest together into one handy bow. Mark Barton
What a nice story, Mark, thanks for sharing!
I went from having almost zero knowledge of what trigonometry is to having an incredibly intuitive understanding. Thank you.
Wait til you experience Trig Identities
It's incredibly easy. I don't know what about it trips people up. It's literally memorizing formulas and algebraic manipulations of said formulas.@@rpruneau68
FLASH CARD/CHARTS/FORMULAS TIME STAMPS
5:43 trig functions (SOHCAHTOA)
7:39 trig functions (reciprocals)
11:18 quadrants (Cartesian Plane)
14:49 chart (Radians)
20:13 formula (Pythagorean Theorem)
24:42 3 numbers (Unit Circle)
I saved your trigonometry course and I will try to finish it. Despite some of the math I will study would not be use in my daily life someday. I still would love to be enlighten and enjoy learning with it.
Thank you for the time stamps! Very helpful. :)
@@JeremyMcElhonegood luck for your exams lil Jeremy :)
Best trigonometry class that I have ever sat in, man, we were never taught like this at all, it's like our teachers never wanted us to understand this concept or maybe they never understood it themselves in the first place so we're doomed. Long live Sir Davis.😊😊
Or maybe they said the same thing but you didn’t listen to them.
Just an intro. Spherical trigonometry will be on the test.
@@aquarius4953 Or maybe the teacher had explain it, but in a complex way that the students are confused.
@@aquarius4953 nah
@@aquarius4953 you sound like a frustrated teacher
this might be embarrassing to say, but I'm in my first year of college/uni and this is the FIRST time in my life that I have ever understood trig! It's one thing to know math, and another one to teach it, and you sir, know how to TEACH!!
First time - I understand this on a visual matter. Instead of learning formules without knowing what I was learning. I agree with another respons that you should have 1M views for this YT video.
Just a stunningly great tutorial. So many kids in 99% of high school literally quit school, because poorly taught math courses like Trig rips their soul. This should have 1 billion views. Your video should be a pre-requisite for ALL middle and high school math teachers, and ALL Freshmen college students. Seriously!!
You, Mr Davis, Sir, are an absolute genius! You are able to teach a not-so-easy and intimidating concept to make is as easy reading a road map by using its legends!! I'll gladly pay to join your Trigonometry classes (probably other math classes, too). Thank you, thank and thank you again!!
Thank you so much, I think I'm blushing!
@@DennisDavisEdu You have what many instructors lack which is the ability to teach knowledge to others. Thanks for sharing, but I would purchase a course from you.
I agree 100%
Sir excellent.. Which software are you using?
This video is a masterpiece! It deserves to be running on continuous loop in the Metropolitan Museum of Art.
after years of my life spent not understanding trig, this video finally made it click. i’m a visual learner and have a hard time with math because of this, but your teaching style makes it so much simpler to understand! THANK YOU!
I'm a visual learner too Paisley. I'm creating videos I wish I could have seen when I was in school. I often thought "If only someone would have explained it this way I would have understood much better!" So that's what I'm trying to do! I'm glad you found it useful. I've just posted a full trig course that goes into more detail and follows the same graphical teaching style. Happy learning!
@DennisDavisEdu I can not express how much I appreciate this, I am gonna enter high school next year and have been dreading trignometry since 4th grade, but now with your course, I can complete it ahead of time! You are helping millions of people learn, keep up the good work, and thankyou for your contribution to humanity❤
THIS. IS. BEAUTIFUL!!! The applied mathematics approach is the only real way for many of us to learn. These basic foundations really help improve my CMM and GD&T knowledge. I'm SO happy to have found this series and cannot wait to jump into the Statistics course before taking my Six Sigma exam. Thank you so much for taking your time to do this and I hope that your channel grows so that we have more resources like this! You and TheOrganicChemistyTutor are changing the game!
Thank you very much ButtonMasher! I'm glad you find my videos helpful and your kind words mean a lot to me.
@@DennisDavisEdu I must say so too, I'm impressed and very thankful. Just started 10th, and very afraid of trigonometry, and u cleared the whole chapter for me before my teachers even got to try. Even if they do, they would just drag on the chapter for 2 weeks where all the students would be told to memorize everything, but in just half an hour, you cleared the whole chapter without telling me to memorize anything, u definitely earned a subscriber
This deserves millions of views.
My teachers told me to cram T-raios without explaining what they actually are, and that's where this becomes annoying. Thank you very much for providing such a great video learning by visualisation and understanding can make anything easier.
T-raios are my favorite cereal. A little milk and sugar and Great!
Why, when there is so much more to life than videos repeating grade school classes?
Well my math teacher at school does the same.
I’m just letting you guys know that I’m not even in school for anything, I’m watching this because it’s available and that’s what I find wonderful. This person for free made this and has probably warranted someone a career that pays them 100k$+.
Excellent presentation. I never had Geometry and was homeschooled and now I'm in college trig. This tutorial is a lifesaver and better now than never although I wish I'd seen it 2 weeks ago before class started. Appreciate you creating this content and look forward to watching your other vids.
Yeah, "homeschooled" means you'll be behind for the rest of your life. Sad, really.
homeschooled lol
I've been out of high school for 19 years, and I stumbled upon this video. I am still absolutely blown away by mathematics and the relations of numbers to each other. Thank you for this lesson.
Hey Dennis - Where were you 55 years ago, when instruction like this would've changed my life! I am so jealous of the Kids these days with their access to Instructors like you and the clarity of that instruction. Now I'm using this to catch up, review and explore so many new and exiting fields of interest. Thank you so much.
Thank you Mark for those kind words. It's never too late to learn something new! I agree with you: Today anybody can learn anything they want for free. Not at all like when we were kids.
I know what you mean. I scour youtube for content like this. It's pure gold.
I salute you sir.No teacher has specified those xy coordinates as you did.They just draw the circle and give those figures.
I swear my teachers just show how to solve problems, NOT how to understand them, and understanding is the basis of higher maths.
Thank you so much for this video. It helped alot and is an incredible source of knowledge and understanding.
Learnt this area of mathematics 50 years ago. The teachers then did not introduce the subject in the way you have done. They just started off with the definitions and jumped into problem solving. Such method was a nightmare to students. Your way is simple and lucid.
Daniel, I wish I could take this video back in time 20 years. You made me understand what took me over 24 months back in high school to memorize so I could pass an exam, and you did it in five minutes.
Sir you are amazing. You have demystified trigonometry in 30 mins. I must say that I am now in love with trigonometry. Sine, cos and tan have now their own personalities. They are tangible and very much useable. I wish calculus and imaginay numbers could also be conceived like this.
I'm nearly done with my math degree and I've been using trigonometric functions and the unit circle literally everyday for years.
I came here to learn the basics so I can use trig identites, differentials, and integrals without memorizing. This is such a good foundation. thank you
You have no idea how much you have helped me. I'm taking a fast paced TRIG class in college and haven't done trig since junior year in HS and was completely lost until this. The course is suppose to cover all of trig in 5 weeks :/
I'm 50 years old and I back in high school, I had to repeat Algebra so, I never had trigonometry. I really wish I did because I think this is a fascinating subject. Good thing for UA-cam and videos like this made by someone who knows and can explain the subject, to make it possible. Great video!!
The best explanation I've seen on UA-cam by far. I wish I saw this before my trig class started!
Before I watch this, I've never taken a trigonometry course before. I was a year ahead in getting to Algebra in grade school but even now in college, I'm still only advanced as far as Algebra w/ Communications, which from what I can tell is essentially "College Math For Idiots: The Class".
And the problem absolutely is visualization. In my sophomore year of high school, my geometry teacher was also my soccer coach, and he would use soccer to visualize math in class and basic math to conceptualize soccer and drill formulas in practice. He was without a doubt my favorite teacher in all of school who wasn't also teaching music. (If you happen to watch this video Coach May, Hi!) But he was my only math teacher after my 8th-grade year bothered with it before my current math course.
Algebra 1 and 2 I just couldn't grasp them conceptually because drilling formulas is ALL that so many public schools do. Why do the numbers act the way they do? How do all of these letters relate to each other? Why is Coach May the only one who seems to be able to tell me what y=mx+b MEANS when it's the formula for a slope? Because eff you, read the formula again and follow the steps, that's why. Only now that I'm in college I seem to be finally grasping Algebra on a conceptual level because my Professor actually drills problems in class, and writes EVERYTHING on the board to connect every term in the problem. I'm still having some trouble actually following the steps in the right order to get the right solution, but tutors have been a good reinforcement, and I'm genuinely starting to improve. UA-cam videos about math make it engaging and fun for once in a way I haven't felt since I was making multiplication tables. I'm finally starting to see how engaging math can be again, and the fact that the wonders of math stop being explained conceptually after you're finished learning basic arithmetic in public school ought to low-key be criminal.
So thank you. As I prepare to watch this video as my very first exposure to real trig, I know I'm not going to understand all of this for probably a long time. But I'm confident by the sentiment of the title alone that what I'm about to see will be engaging, and further spark this newly found passion, even if passion hasn't yet translated into skill on my part.
That's a nice story, thanks for sharing. I agree visualization is the key to deep understanding. Now I'm afraid this short overview will disappoint you because it is not a deep, thorough introduction. It just scratches the surface visually.
For better, deeper trig coverage, please see my multi-part playlist linked in the description.
Happy learning!
You have my respect!
I am 70 years old and I wish my math teacher had shown your methods, we were always being told to memorise, memorise, memorise!
Can’t beat a little brain exercise!!!!
Thank you very much!
An ounce of understanding is worth a pound of memorizing!
If I had watched this in high school, I probably would’ve Aced the class! The visuals are excellent. Thanks again! 👍
Videos like these are the reason I watch UA-cam.
This is the first time I’m commenting on a UA-cam lecture video and that’s cos I’m beyond wowed. This is hands down the best lecture I’ve had in my life. Thank you! 🙏🏽
Wow. I thought I was the best teacher when it came to introducing the ideas of trig so as to not be intimidating, seem like common sense, and easy to remember (by simply figuring out.)
After 30 years of this, I take off my hat, and bow to the man who has bested me.
I’m an English as a second language teacher. I love these memory hacks. It helps to give first time learners edge of confidence that they could learn further. Truly the heart of a teacher.
You just save me a ton of time for studying!! i am a "figure out" person, i cant just "memorize" things and take them as "face value" there must be a REASON for them, and you just prove it!!
Thanks!!!!
Thank you! This video is incredible. Not only it demystified trigonometry but now I actually understand. Like someone else mentioned, this is "Gold Standard" teaching.
Yes sir,you are a GENIUS.TEACHER..THANKS
11:35 imo, this would have been a good spot to shoehorn the "right hand rule" in as a memory aid for the direction that the angle sweeps positive as that is also a very fundamental concept much later. "Just point your right thumb at yourself and notice the direction your fingers curl". This will also address any potential ingrained mental bias towards clockwise motion.
I never understood the conversion of degrees to radians intuitively, and now I’m a master at it.
As corny as it is, you did what my math teachers could not.
Thank you so much.
Watching this video solidifies in my mind, just how much time was wasted going to school. I was stuck in Trig for 4 years, never understood it as well as I have now in this short 30 minute video. I appreciate what you're doing to help accelerate our up-and-coming generation. I just hope it isn't too late.
Sir, im father aged 45 of a boy from India who is in grade 10 and i amazed if i could see it when i was in his age. My son finds it helpfull too. Hat's off to u sir.
Best video ever. Sir, you're an absolute legend. I'll rewatch this video many times from now on. I could understand in two days a topic that I was so afraid of for months. I'm actually in precalculus and I this has saved my life. Thank you, sir. I'll watch your other content and subscribe! Hope you continue being a math hero! 👏🙌
Thank you Manuel for your kind words. I think my big Trig series (see description for link) is so much better than this video, but this one gets all the views and nice comments. That series has 80 videos right now, but every day this long-form overview video gets more views than those 80 combined. Well, the customer is always right!
Thanks again, I'm glad you were able to overcome your fears. A little knowledge can give confidence, and confidence fights away the fear!
The way you are able to see patterns and explaining them really helps me with understanding this. Thank you!
Excellent method of teaching , should be the " Gold Standard "
Agree
Should be the standard
I always did trigonometry just by memorizing but at the same time did wonder what actually they are and how should I visualise them, but after watching your video, my years of questioning myself has finally come to an end. Thank you so much.
My new trig series has been posted...
ua-cam.com/video/NBC4ZvCt2Lg/v-deo.html
It is a series of 46 mini-lectures with (I think) improved style and clarity.
It is more in-depth than this simple overview.
Dennis
Is this still essential or should I skip this and start there?
The series won't be completed for some time, but it is much more in-depth. This one covers the essentials, but I had to leave some stuff out, like the most famous equation in trig: cos²θ +sin²θ = 1. For quick overview, stay here, for more in-depth, see the series.
Or watch 'em all!
@@DennisDavisEdu Decided to watch both 🤷🏾♂️
I’m kind of loving this channel. TVM professor David
What would I do without you?
very clear and with very helpful mnemonics
This was more helpful than my last 3 math teachers. *Thank you.*
No other explaination of this trigonometry concept can match this video ! This is THE BEST❤
Why this guy has only 125 subscribers?! Really brief, clean and complete explanation!
probably because he has only two videos. why woud someone subscribe to an account with no more content
I have posted more videos now.
@@DennisDavisEdu glad to hear that!
You are a gifted teacher. I am 48, was trying to find information to teach my daughter. I wish I was taught this when I was in school.
Check out my longer trig series linked in the description.
It's more of a full semester's worth of information taught in the same style.
This video is just a high level overview.
It sounds like your daughter is in good hands.
Best wishes to you both!
I didn't think you'd make it but you came through. You got me over a difficult hurdle.
AI engineering student: Thank you for breaking that down in simplest terms- you've made a significant improvement in my comprehension of the unit circle and what exactly the trig functions are and what they mean. I truly appreciate this knowledge- it definitely beats trying to memorize like a fool. I crave to comprehend always.
Thank you so much for this.
13:14 I never was taught that, instead I was taught to remember some formula on how to convert form rad to degrees but never got an explanation why
I was about to rip off my maths books and throw them away after how I suffered but sir you LITERALLY SAVED ME WHOLE LIFE THANKS ALOT this is the best trigonometry lesson I have ever leaned
Highly recommend. You will never have to memorize the Unit circle again. Brilliant way to teach. Thank you very much.
But I still try to memorize it 😩
@@sucdilucky3795 try it a few times. it might help.
There's not as much to memorize in trig as you might think. If you understand the concepts, you can figure out most things quickly and with less stress than memorizing. And you enhance your understanding!
@@DennisDavisEdu Yes, agreed. After I watched your video a few times, I started to understand the concepts.
the last part with the small, medium, large is a big help. That is really easy to remember and use. I was struggling with trig when they appear on graphing problem in class, now I feel like I can solve them on my own. Thank you very much!
very underrated, very good content. keep up the good work!
It was lovely to return back to school times..
Thank you. Now I can flex my math skills in trig this new school year when Im taking trig
Oh my God! I hadn't expected this video to happen. It has helped me with a mountain of exercises since I was in 12 grade, a junior high school, I had learned Physics in general, and trigonometry in particular. At that time, I was stuck by the death circle, 'cause I couldn't remember the numbers well. But when I watched Dennis Davis's video, I completely changed my mindset to the Trig. It's easier to have a deep understanding, and, of course, Davis I'm now always visualizing not memorizing as you said! Anyway, Thank you so much for making an incredible video!
I was only taught the sin, cos and tangent. While I knew about the other three, I was never introduced to or used them. Thank you for a most informative class!
Me too, and happy with it. Why introduce yet another function name for say 1/sin(x)? For me sin, cos and tan, their series expansions, the complex exponential and Euler's identity are all trig I bother to remember.
fourth year math undergraduate, worked with discrete math for a while but taking an interest in analytic geometry and this was the perfect reintroduction to trigonometry, thank you!!
This video on trigonometry turned out to be the most understandable and informative of all that I have seen before. I did not even notice how 30 minutes of the lesson had passed, while I was absorbing the information with interest
3 Years later, and you're still saving lives with these videos! THANK YOU!
This is such a phenomenally informative video. The visualizations make trig easy to learn. I am very pleased with this quality content.
Good sir you are a blessing I've been avoiding trigonometry for more than a year because of the unit circle, but you taught it to me so easily i can not sufficiently express my gratitude to you good sir THANK YOU VERY MUCH
The basics of Trig are no longer a conundrum. This video is an absolute GEM 💎
Stumbled into this one was was blown away. Out Standing Troop. Beautifully elegant and simple. Yes boil it down. The graphics were great. Cutting board great. Help set the perspective with the origin. Brings back do much. Today retired but gmdijnv CAD for 3D printing parts for my 1950s model train. Still beef to know angles and ratios but oh My God so long ago. This was an awesome refresh. Thank you. Dennis
Excellent stuff!… I can appreciate the sheer number of hours it must have taken to produce this. Subscribed!
You explian very well and it was useful. thank you very much
Thank you! Why you stopped making more???
Your teaching is just amazing... you should go ahead ... you will rock!! (:
excellent! these are the same sorts of tricks I came up with to avoid memorizing things too. It's not laziness, it's about being practical. I recognized in high School that I would never remember everything forever, and that the less I had to memorize, the more likely I would remember it long term, and focused instead on being able to use those basic core concepts to recreate or solve for anything else I needed later on. I didn't learn the concept of "first principles" until well over a decade later in life, but that's basically what we came up with.
Thank you for the high quality lesson! It helped a lot!
Words can’t describe how this video helped me understand the concept of trig functions further.
Thanks a ton!
You did a fantastic job explaining everything! Thank you very much for all the work you put into the video it helped a lot!!!
Thank you Valadez, you lifted my spirits for the day!
Excellent. I love your emphasis on knowing how to visualize things rather than memorizing.
Early childhood education needs to be flooded with these kinda teachers.. the world will be a better place 🙂, A nation of thinkers given such a stepping stone breeds better scientists
WOW. was DROWNING in trig, so scared of failing - I have a genuine understanding now!! THANK YOU for your EXCELLENT video! ❤
the perfect tone, perfect pace and perfect representation.....thanks for this simplified tutorial
This is by far THE BEST explanation on Trigonometry I have ever seen in my life!
Dude you are the ONLY teacher who knows how to convey this stuff well
7:40 - "Whatever you can memorize, you will easily forget. But what you know how to figure out, that you can do forever." 👏
The key to everything.
We learn best through Discovery…
NOTHING beats experience …❤
This is the most visual-spacial / logical step by step explanation that every student needs. This is exemplary.
I was about to give up on trying to find someone who could break it down. You are the best.
If you want to be good at calculus, you have to be good at trig because it is the foundation for understanding concepts of basic calculus, advanced calculus, linear algebra and physics
No, knowledge of trigonometry is not needed to understand calculus. In calculus you will perform "operations" on functions. (The operations are called differentiation and integration).
You'll probably start out with linear and polynomial functions because they're the easiest to understand the calculus "operations". But eventually you'll get to functions that include trig functions in them. You don't need to be a trig expert to do this, and trig is certainly not a foundational requirement to learn calculus.
When you get to the trig functions, it would probably be helpful to see the graphs of the trig function in your head or be able to sketch them out quickly. See video TR-18 in my more detailed trig series here: ua-cam.com/video/f99P31SAsek/v-deo.html
every second of this video, exudes sooo much knowledge that to even manifest it on plain paper is gon' take another course of it's own like I LOVE IT.
outstanding sir i was very much stuck at sea without a paddle and now i feel like i was over thinking most of it. one of the best maths videos i have come across. Thank you.
I was an extremely good math student in high school. Won math tests and stuff... not braggin'... maybe braggin' a little.
Anyway, I took calculus 2 in high school, but there was only one class that ever really frustrated me... trig.
Trig was the first class that felt like memorization and math to me has always been about conceptualization... not memorization.
Anyway, I had to develop the conceptual tools myself, and it was the hardest math class ever for me...
I wish I'd seen this video when I was taking trig. My advice to anyone... watch this video enough times that you understand every single word.
If you can wrap your brain around this video, you will be able to pass an end of course trig exam. You will only need a few more conceptual tools and memorized formulas to ace it.
This video is enough framework to get you most of the way through the course.
Fantastic job Mr Davis. Don't take this video down. When my kids are old enough, they WILL be watching this video.
Just one word. Outstanding!
I’m an IT student and It’s too late that I’ve just discovered your channel. Now I go back here to get a refresher about the unit circle because of Calculus. This is way too easy to understand. Why did I come here late😢 In just a few minutes, I easily memorized how you delivered everything😢 too late…
Thank you.
Took trig as a jogh school junior.
It helped me to understand construction and also ballistics used by the US Marines and sailors