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

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.

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.

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'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.

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.😊😊

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

I went from having almost zero knowledge of what trigonometry is to having an incredibly intuitive understanding. Thank you.

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.

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.

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.

This video is a masterpiece! It deserves to be running on continuous loop in the Metropolitan Museum of Art.

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!

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 KZfaq when I was a kid

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.

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

This is the first time I’m commenting on a KZfaq 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!

Mr Davis, Thank you for making this so clear in this step by step "unit by unit" manner. You present each concept to the viewer as if they have little to no understanding, and tip-toe through each. Absolutely fantastic. Please keep your videos coming.

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!!

The best explanation I've seen on KZfaq by far. I wish I saw this before my trig class started!

This is the first time I’m commenting on a KZfaq 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! 🙏🏽

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!!

This golden content, keep it up! With this single video (and without taking notes) I fully understand the concepts you have explained just by watching this video once! This is amazing, this deserves tons of appreciation. Keep it up!

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!

This was a great supplementing tool for a lot of what I learned in Precalculus so far! No more drawing out unit circles for me! Visualizing Pythagorean theorem also never occurred to me before. I'm excited to put this all into practice and save some time. Big ups! 🙌🏻

Words can’t describe how this video helped me understand the concept of trig functions further. Thanks a ton!

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.

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.

I salute you sir.No teacher has specified those xy coordinates as you did.They just draw the circle and give those figures.

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.

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 :/

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.

The way you are able to see patterns and explaining them really helps me with understanding this. Thank you!

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$+.

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.

I didn't think you'd make it but you came through. You got me over a difficult hurdle.

the perfect tone, perfect pace and perfect representation.....thanks for this simplified tutorial

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!!!!

This is such a phenomenally informative video. The visualizations make trig easy to learn. I am very pleased with this quality content.

Excellent stuff!… I can appreciate the sheer number of hours it must have taken to produce this. Subscribed!

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!

Upon completing grade 13 trig I doubt that these concepts were this clear in my mind. An art, good teaching.

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! 👏🙌

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.

3 Years later, and you're still saving lives with these videos! THANK YOU!

Excellent. I love your emphasis on knowing how to visualize things rather than memorizing.

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.

very underrated, very good content. keep up the good work!

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 studying for my FE exam and never in my life have I ever understood trig this well. I wish these sorts of videos existed years ago when I struggled with math in high school through college. I love the concept of visualizing because I'm a visual person and most teachers don't teach that way. I felt like I always needed to memorize things I didn't even understand completely because I could not see it in my head. From the explanation of a radian, and seeing how and what it is and showing us the break down of the degrees vs the radians to the unit circle explanation was the best! I remember in one of my math classes I would spend forever either memorizing the unit circle or squeezing it into a corner on my cheat sheet lol. I always wanted to know the whys and teachers don't usually teach the whys or show us how we got certain values such as the ones on the unit circle. I'm looking forward to learning from more of your videos.

This was more helpful than my last 3 math teachers. *Thank you.*

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.

Wow, this was amazing. The calm voice, clear explanations and easy rules of thumb. Awesome!

Simply brilliant! Clear, systemic and direct. Congratulations

Thank you for the high quality lesson! It helped a lot!

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.

Videos like these are the reason I watch KZfaq.

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.

My new trig series has been posted... kzfaq.info/get/bejne/hKhzZ72nqNqWfJs.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

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

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!

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.

Why this guy has only 125 subscribers?! Really brief, clean and complete explanation!

Thank you. Now I can flex my math skills in trig this new school year when Im taking trig

Dennis, thank you a lot for this video. Wish I had been taught trig like this many years ago, everything was laid out so clearly!. You're an excellent teacher, greetings from Buenos Aires - Argentina.

This is by far THE BEST explanation on Trigonometry I have ever seen in my life!

Gonna comment to boost the algorithm. One of the best math vids out there. Thank You!

I am an artist and have been intimidated by math all my life. This makes at least the introduction to trig manageable. Thank you for explaining it in such a visual and clear way.

This is the most visual-spacial / logical step by step explanation that every student needs. This is exemplary.

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 KZfaq and videos like this made by someone who knows and can explain the subject, to make it possible. Great video!!

Excellent method of teaching , should be the " Gold Standard "

The basics of Trig are no longer a conundrum. This video is an absolute GEM 💎

You channel was simply listed on my youtube screen. I took trig in HS and one course in college. It's always intrigued me. As a sailor using celestial navigation I should be very familiar with it. I also have a book on spherical trig ... wow, a little over my head, but that's what navigation is based on. I hope to learn a lot from your channel.

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.

Highly recommend. You will never have to memorize the Unit circle again. Brilliant way to teach. Thank you very much.

Thank you! Why you stopped making more??? Your teaching is just amazing... you should go ahead ... you will rock!! (:

I wish I knew you when I took trig in high school. Very helpful and would have helped immensely. Thank you so much for sharing. Thumbs up and subscribed. 30 years later, I find I’m having to relearn forgotten math needed for new job role. Thanks again for providing clarity on this

Professor Davis, thank you for a solid explanation of the classic Trigonometric Concepts in old fashion Mathematics.

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.

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

High school Trig class 50 years ago. I finally understand. WOW ! Using this knowledge in my hobby machine shop. I’ll review this with the 6yr old grandkids so they grow up with the concepts. Thank you Mr. Davis Larry

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!

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 for this comprehensive and very simple visualization of trigonometry, was struggling with it for my CS uni prep but now I think I can ace this section of the entry exam, THANK YOU VERY MUCH!

I graduated in 90’ and I had trig my freshman year and this’s exactly how my teacher taught us. I loved math!

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!

Thanks I never knee the sin and cos were derived from soh cah toa, where hypp = 1 so it can be ignored. Very cool thank you! Just memorizing 1 circle = 2π radians :)

Outstanding video and superbly well narrated. Thank you for bringing crystal clarity to trig.

This video is a LIFE SAVER. I couldn’t grasp the concept of the unit circle but this video explains it clearly. THANK YOU

Whithout Visualisation this gave me a Headache.. Now are you here to give me Nightmares !! 😂😂😂

I was about to give up on trying to find someone who could break it down. You are the best.

You are the friggin MAN!!! I've been fortunate enough to have had some amazing Maths teachers over the years .. I've loved it a bit more everytime .. you have made that list in just 30min! You blew my mind SO many times with things I'd "learned" only to realize I'd "Remembered" instead!!! That "Long / Medium / Short" trick is NOTHING SHORT OF GENIUS!!! I can't thank you enough .. but THANK YOU!!!

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

This video is exceptional and the best one I've ever seen - it's clear and easy to comprehend and remember

From the analogies to the simplistic way he explained it all, he nailed it. best math video I've ever watched,

This was the most intuitive explanation I have come across. Thank you

Respected Sir... This video should be made mandatory for all students studying Trigonometry and even Complex Numbers !! You explained it very well. There should be a separate award for teachers who can teach complicated Mathematical concepts so easily. I am sure you would win every year. Thank you for your efforts !!

Thank you so much for your absolutely outstanding work! I cannot recommend your series on trigonometry enough. It was great fun to watch and demonstrated what the future of education should look like. Bravo!