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.
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!
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.
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!
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. ruclips.net/video/Dsf6ADwJ66E/видео.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.
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.😊😊
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 RUclips when I was a kid
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. 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
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.
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.
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 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!!
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 the first time I’m commenting on a RUclips 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!!
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.
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.
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.
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.
I love to hear that Mr. McCallister. I'm only 55, but I've been studying trig for the last 2 years. I mean I really do love hearing you say that, because my mom sits around doing crossword puzzles all day. It keeps her occupied, but I think she gave up. Seeing you excited about learning is how I want the rest of my life to be also. Thanks for your comment, it is an inspiration to the outlook of my future.
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’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$+.
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.
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.
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.
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.
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!
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 RUclips and videos like this made by someone who knows and can explain the subject, to make it possible. Great video!!
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.
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.
Utterly Brilliant. I am 80 and have been good at Maths all my life. BUT in 1950s GCE Trigonometry and Arithmetic was one exam, Algebra and Geometry were 2 others. I was utterly baffled when I got to university and the Economics lecturer used trigonometric functions to solve algebraic equations. As for Radians, they were never taught and would often have been useful. the 3 4 5 triangle has been my lifesaver many times but now it means so much more.
Contrarily, I was a highschool dropout that became a carpenter & the 345 triangle was the only trig I learned on the job, to square up a house. For the first 10 years of my career that was all I knew. Then an educated friend taught me the Pythagorean Theorem. Now here I am on youtube learning all that good stuff I missed out on. RUclips is such a good tool. I used to be angry at my teachers & the school system, but I have learned it all worked out just fine. I am truly content.
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!
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’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…
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!
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!!!!
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 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!
this is life-changing, my teacher never go this deep but tell us to memories, I'm always scare of unit circle cause it didn't make sense for me in high school. But hanks to your videos I have a better understanding of math now.
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
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.
My new trig series has been posted... ruclips.net/video/NBC4ZvCt2Lg/видео.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!
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.
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
OMG! The whole video blew my mind🤯. THANK YOU!!! I'm hooked I'll watch an hours a day of your trig playlist. Do you plan on doing a pre calc, calc 1, calc 2, calc 3 playlist???
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.
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
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.
That last section with the small, medium, and large values is super helpful. It works well with the pattern I've used to remember the angles, and is a nice visual guide. Thank you!
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
This was so helpful. There was just 1 concept I couldnt fully visualize and you've cleared it up for me in the unit circle portion. Also the Co memorization trick very clever.
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
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.
Wow! 🥳👏 I'm finally returning to college after 28 years away. I was unable to complete my sophomore year the first time because I had undiagnosed narcolepsy & lived half my life in another dimension. In 2005, I figured out the cause and recovered, and I'm finally in a place to start classes again. I'm pursuing a degree in Electrical Engineering, and I came here because I need a refresher as I re-take Calculus yet again. I had learned this before, but your clear visual explanations and tricks are AMAZING! 👏👏👏 I swear you just made a huge difference in my ability to understand this and grasp problems much more quickly. THANK YOU SO MUCH! ❤🎉❤🎉❤
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!
WOW I'm ASTONISHED by the quality of this video. I'm a maths teacher in an academy and I learned a lot of things. Incredibly well explained and organized and clear. Thank you very much
Beautiful work... I finally truly understand how the unit circle works and can now draw it on a blank paper simply based on understanding how to get all of the components rather than having to memorize these.
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! 🙌🏻
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!!
I've been struggling with learning the unit circle and measurements in radians. Thanks to this video, I think I might actually have a better understanding of these concepts! Thank you!!!!
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 😤
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!
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
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.
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 👍
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. ruclips.net/video/Dsf6ADwJ66E/видео.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.
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 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.
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
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 RUclips when I was a kid
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. 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
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?
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 :)
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!
This video is a masterpiece! It deserves to be running on continuous loop in the Metropolitan Museum of Art.
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!!
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❤
No other explaination of this trigonometry concept can match this video ! This is THE BEST❤
This is the first time I’m commenting on a RUclips 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!!
The best explanation I've seen on RUclips by far. I wish I saw this before my trig class started!
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.
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.
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.
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.
I'm 81 years old, and because of your explanation, I now understand the basics of trigonometry. Thank you.!
I love to hear that Mr. McCallister. I'm only 55, but I've been studying trig for the last 2 years. I mean I really do love hearing you say that, because my mom sits around doing crossword puzzles all day. It keeps her occupied, but I think she gave up. Seeing you excited about learning is how I want the rest of my life to be also. Thanks for your comment, it is an inspiration to the outlook of my future.
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’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$+.
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.
The way you are able to see patterns and explaining them really helps me with understanding this. Thank you!
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.
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.
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.
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!
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!
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 RUclips and videos like this made by someone who knows and can explain the subject, to make it possible. Great video!!
I didn't think you'd make it but you came through. You got me over a difficult hurdle.
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.
very underrated, very good content. keep up the good work!
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.
This was more helpful than my last 3 math teachers. *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.
Excellent stuff!… I can appreciate the sheer number of hours it must have taken to produce this. Subscribed!
Words can’t describe how this video helped me understand the concept of trig functions further.
Thanks a ton!
This is such a phenomenally informative video. The visualizations make trig easy to learn. I am very pleased with this quality content.
Utterly Brilliant. I am 80 and have been good at Maths all my life. BUT in 1950s GCE Trigonometry and Arithmetic was one exam, Algebra and Geometry were 2 others. I was utterly baffled when I got to university and the Economics lecturer used trigonometric functions to solve algebraic equations. As for Radians, they were never taught and would often have been useful. the 3 4 5 triangle has been my lifesaver many times but now it means so much more.
Contrarily, I was a highschool dropout that became a carpenter & the 345 triangle was the only trig I learned on the job, to square up a house. For the first 10 years of my career that was all I knew. Then an educated friend taught me the Pythagorean Theorem. Now here I am on youtube learning all that good stuff I missed out on. RUclips is such a good tool. I used to be angry at my teachers & the school system, but I have learned it all worked out just fine. I am truly content.
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! 👍
YOU HAVE NO IDEA HOW GRATEFUL I AM FOR THIS VIDEO!!! THANKS SO MUCH.
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’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…
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.
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!!!!
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.
Professor Davis, thank you for a solid explanation of the classic Trigonometric Concepts in old fashion Mathematics.
Thank you. Now I can flex my math skills in trig this new school year when Im taking trig
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!
Wow, thanks! You gave me a boost for the day!
@@DennisDavisEdu Your welcome, keep up the great content!
this is life-changing, my teacher never go this deep but tell us to memories, I'm always scare of unit circle cause it didn't make sense for me in high school. But hanks to your videos I have a better understanding of math now.
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
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.
My new trig series has been posted...
ruclips.net/video/NBC4ZvCt2Lg/видео.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?
3 Years later, and you're still saving lives with these videos! THANK YOU!
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.
Excellent. I love your emphasis on knowing how to visualize things rather than memorizing.
Thank you for the high quality lesson! It helped a lot!
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
Thank you! Why you stopped making more???
Your teaching is just amazing... you should go ahead ... you will rock!! (:
OMG! The whole video blew my mind🤯. THANK YOU!!! I'm hooked I'll watch an hours a day of your trig playlist. Do you plan on doing a pre calc, calc 1, calc 2, calc 3 playlist???
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! 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.
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
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.
I felt being hug with this video, God bless you Dennis, thanks a lot for this clear and patience and easy way to understands this concepts.
That last section with the small, medium, and large values is super helpful. It works well with the pattern I've used to remember the angles, and is a nice visual guide. Thank you!
Great to hear! Thanks!
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
This was so helpful. There was just 1 concept I couldnt fully visualize and you've cleared it up for me in the unit circle portion. Also the Co memorization trick very clever.
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
I was about to give up on trying to find someone who could break it down. You are the best.
Wow, this was amazing. The calm voice, clear explanations and easy rules of thumb. Awesome!
the perfect tone, perfect pace and perfect representation.....thanks for this simplified tutorial
This video is exceptional and the best one I've ever seen - it's clear and easy to comprehend and remember
This is by far THE BEST explanation on Trigonometry I have ever seen in my life!
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.
Wow! 🥳👏 I'm finally returning to college after 28 years away.
I was unable to complete my sophomore year the first time because I had undiagnosed narcolepsy & lived half my life in another dimension. In 2005, I figured out the cause and recovered, and I'm finally in a place to start classes again.
I'm pursuing a degree in Electrical Engineering, and I came here because I need a refresher as I re-take Calculus yet again. I had learned this before, but your clear visual explanations and tricks are AMAZING! 👏👏👏
I swear you just made a huge difference in my ability to understand this and grasp problems much more quickly. THANK YOU SO MUCH! ❤🎉❤🎉❤
I'm glad the video is helpful! Make sure to check out my Calculus video!
@@DennisDavisEdu I will! Thank you! 🙏💝🎉
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!
WOW
I'm ASTONISHED by the quality of this video. I'm a maths teacher in an academy and I learned a lot of things. Incredibly well explained and organized and clear.
Thank you very much
This is the most visual-spacial / logical step by step explanation that every student needs. This is exemplary.
I'm so glad I watched this video.
Among so much hollow content, your video is like an oasis in the middle of RUclips.
Thank you so much sir!
Very well presented! Excellent use of GRAPHICS and COLORS...and GREAT VOICE, too. THANK YOU 🙂
Amazing video. I'm a maths tutor and I'm going to send this to all my kids. Thank you
Videos like these are the reason I watch RUclips.
Beautiful work... I finally truly understand how the unit circle works and can now draw it on a blank paper simply based on understanding how to get all of the components rather than having to memorize these.
Perfect! You gave me happiness today!
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! 🙌🏻
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!!
I've been struggling with learning the unit circle and measurements in radians. Thanks to this video, I think I might actually have a better understanding of these concepts! Thank you!!!!