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.

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.

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.

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.

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

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, 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.

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.😊😊

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

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 UKposts when I was a kid

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

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

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

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.

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

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

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.

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

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! 🙌🏻

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.

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

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.

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

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.

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

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

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

Simply brilliant! Clear, systemic and direct. Congratulations

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 :/

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!

Best video on trig ive ever seen. I built all my trig from this10 years after high school. If i were to create a course or channel this is what i hope to emulate.

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!

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

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.

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

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

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.

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!!

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'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.

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

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

You're a very good teacher. Text books and school teachers are pretty horrendous at explaining more complex maths topics, you break it down step by step so anyone can understand and remember (visually) thank you.

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

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

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.

Realised a very similar thing a year after intro to unit circle. BY FAR the best way to understand trig

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!

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.

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

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

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

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.

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.

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.

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

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! 👏🙌

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

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

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.

This video integrates trigonometric math basics taught in many schools in separate lessons of segmented syllabus in ways that paralysed young learners - paralysis by analysis. It is great as an introduction video before and after trigonometric classes. IT serves as a beautiful 'end in mind' learning outcome that both teachers and learners can relate to, work towards and achieve together.😊

Wow. This video would have saved me so much time in high school. Thank you for taking the time to teach everyone in such way that is easy to remember! This is making my return to math for college much easier!

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

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.

Thanks for continuing to say "don't memorize." As you say, knowing how to derive the details makes this SO much easier.

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.

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.

My new trig series has been posted... ukposts.info/have/v-deo/hnJ0aJCteqpjrZs.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

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!!

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

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

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

Thank you so much, Mr. Davis! After seeing the pattern for converting degrees into radians, I decided to use multiples of 15 degrees (pi/12 rad). I could go even further and use multiples of 5 degrees (pi/36 rad). This is amazing, thanks for explaining it so clearly!

I started a n OU maths starter degree but didn't have the basics to be able to understand it. This has filled in the blanks. Thanks❤

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.

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

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!!!

Unreal. Days spent memorizing, because that’s what the teacher told us to do. But it’s this easy. Watching this one time gave me a better understanding of trig than all my years of school. Thank you.

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

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

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

Thank you so much! You really made it so simple, I wish i had teachers who could explain at lest half of how well you explained here. You are just excellent.

You did a fantastic job explaining everything! Thank you very much for all the work you put into the video it helped a lot!!!

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 :)

I never leave comments but this video deserves praise! Thank you for the help! It all makes sense now!!!!!!!

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 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!

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!

Enlightening little video. Very direct path to understanding and translating the relationships of of the trig functions to angle and radeon values. Thanks!

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

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

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

Much appreciated, as a visual learner this was very helpful in solidifying the concepts.

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

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

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