❖ Trigonometric Identities: How to Derive / Remember Them - Part 1 of 3 ❖

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

[@harsathabinav.m]

1/4a2b2-1/6ab2c+1/36b2c2.factorize using identities

[@free-energy-systems]

I like this video because instead of saying "memorize" this, you showed what 1 is when adding or subtracting. It is a variable. Thank You!!

[@dattatraybade9929]

.

[@ahmadfaisal4820]

What is key word for memorize these trigonometric identities?

[@Woutouber222]

In 13 minutes I have learned more about identities than I have in school in the past 3 weeks

[@Alex-su9nz]

yeah exactly!!!

[@Xilosphere]

robbybaby1200 Fewer distractions?

[@iankim748]

Max Smith it's because in school, they try to drive it in you by being repetitive... this is a quick lesson that you will easily forget

[@violiningss]

For my school that happens because they try to rush the syllabus on us and don't clear everything out.

[@OpnWrldgmng]

robbybaby1200 I’m gonna say it’s because the school district thinks you aren’t smart enough to learn at this fast pace.

[@princessdiana2414]

I want to thank you SO much for this video. Trigonometry has always been my weakness in math. I'm now in calculus and we're currently doing derivatives of trigonometric functions. This review has provided me with such a great amount of confidence in this unit. THANK YOU!

[@RawDoggin_78]

6 years later and i am in th exact spot as you are, history repeats i guess lol

[@RavenCelestia]

got an exam on monday, im looking for miracles

[@justinlewtp]

who needs miracles when u have Patrick

[@dramawind]

I thought so too but no matter how much Spongebob I watched before the exam I still failed.

[@coolbeans3138]

Raven Celestia SAME

[@rozikhan2744]

got an exam in 20 mins I need jesus 🙌

[@dustinsimmons4418]

how did yall do?

[@TheCatMasterOfKnow]

With every year I go in math I feel more and more like an idiot. Everyone else seems to get it...

[@patrickjmt]

+The CatMaster if it makes you feel any better, I felt just like you. But, I worked my butt off and here I am...

[@PimpMatt0]

I lose my patience every year I go in math.

[@rozikhan2744]

Try physics 😥

[@Whaddif_]

it’s not that they get it, just they’re better pretenders :)

[@bootseen344]

@@Whaddif_ so fucking true

[@MP-wb7sh]

wish my teachers taught me the trig functions this way rather than just telling us all to memorise them. Thank you!!

[@neootukile208]

to all the tutors on you tube thanks, you guys are a big help.

[@hurrdurr25]

Why do they not teach this way in school? All they teach is memorization which isn't teaching at all in my opinion.

[@daple1997]

It wouldnt work as well as you think since at times the teaching needs to adapt for a variety of people, and since most people can barely substract, (it is noted that after a few years after high school people might just forget how to do it). Hence most people wont even understand this connection of equations and memorizing just has to do.

[@prophetic1012]

Just shut up and HOLD THE DOOR!

[@robertwilsoniii2048]

PatrickJMT is a huge proponent of the "just memorize it" and "shut up and calculate" mindest. So I have no idea what you're talking about. I agree with you, more people need to be exposed to the true reasons we do things, but the reason nobody ever does it when teaching is because nobody knows themselves. Real numbers are a great example of why this is; nobody to this very day really understands what a real number is (dedekind cuts are absurd, equivalence classes of cauchy sequences are alright, decimals mean nothing (are arbitrary symbolic systems)). It's pretty fucking stupid if you ask me; everyone just memorizes equations on blind faith like it's a religion.

[@versus13]

Dustine smith HODORRRRR HODORRR

[@A_C2215]

YOU ARE AMAZING! I mean that from the bottom of my heart. the only tutor I could find that explains the small nuances (which are usually the things that trip people up) so well!! Please don't stop making videos. You have a new subscriber :)

[@bryantiu1151]

I don't know what I don't know anymore.

[@MadnessYouSay]

Bryan Tiu 😂😂😂😂

[@mamekuti4044]

Basically you know everything or you're just pure dumb 😂😂

[@bjornjagonos6723]

Bryan Tiu HAHAHAHAHAHHAA

[@roentgen8804]

ify

[@juanvolvoturbo]

Calculus makes me feel like a failure in life.

[@chris-dd6uq]

Taking Calc and not understanding geometry or trig makes me feel like a failure in life.

[@robertwilsoniii2048]

It's not your fault. Nobody alive today really understands "real numbers," which are the "foundation" of calculus. It's all half-bullshit. Don't feel bad.

[@birdobonkers5205]

One year later. Where are you at now? Bet you're making progress.

[@gailykaira]

calc is difficult at the beginning but very very easy at the last part.. the teacher will only teach the shortcuts at the end..

[@palootto4021]

@@gailykaira This is not calculus. This is trigonometry. You must learn trig. before you do calculus.

[@RyuHaruse]

This series literally saved me from the despair of going to college without knowing a single thing of trigonometry... My sincerest thanks!

[@nursyazreenmahdzir3597]

watched all your 3 parts of how to remember/derive trigonometric function . they are all amazing and i can finally understand them very clearly . thank you for the great video !

[@kaileykeenan3018]

Thanks x10^10. You're clear and understandable. I'm taking an accelerated Trig class right now, and lets say...the teacher is a talking book. You are awesommeee

[@RexGalilae]

Your a hero for all of us who once gave up math in high school!! I just want to see your great channel grow even more!!

[@patrickjmt]

@MIT2004 anything in particular?

[@AsteruxGaming]

Thank you so much. I've been struggling to remember these identities for over a year and a half. This video really helped me remember them. I really appreciate what you're doing.

[@Brownie4078]

for real as soon as i start making some money im donating to you you have literally been saving my ass in math this year thank you!!!

[@hniang2]

i never really comment on any of your videos but I always watch your videos to study for my math exams. You are a great teacher. Because of teacher like you, I also want to become a math professor and do Phd in mathematics:D Thank you so much for helping all of us!:D

[@patrickjmt]

thanks for such kind words, i appreciate them ;)

[@alaakhalid96]

I'm taking calculus 1 now in university. first we I begun studying the subject I was a dummy person. I forgot all these trigs, and I didn't even try to understand it where did they come from. now thank to you. I'm able to understand and solve calculus problems after memorizing them with understanding. Awesome!

[@cmhammo2025]

THANK YOU FOR SAVING MY IB MATH GRADE, THESE THINGS WERE GOING TO PREVENT ME FROM GETTING MY IB DIPLOMA

[@Hardstyle_Queen]

For compound angle, I tell myself that cosine is selfish & crazy, only wants to pair with its own "species" aka a clone(tries to find words that starts with C), while sine is always sharing. For tan I know that if it's a + on the numerator, the bottom is minus, & vice versa, as for denominator I know by heart of its signature 1, minus or add the product of tanAtanB, respectively to its signs. 😂 Good video! It helped me on my Pythagorean identities, I was freaking out at first. I recall learning logarithm from this channel years ago, Now I'm back again! 😊

[@patrickjmt]

ha, that is awesome. it is funny how we all find our own strange ways to remember things :)

[@Xxpussydestroyerxx12]

小林雪羽

[@SupremeFallenX]

These hidden relationships make memorizing the identities so much easier! Thanks Patrick! Be my math teacher D:

[@rianshabani9181]

bro thank you a lot, every time that i enter this chanel i know that i found the solution for my problems, and i cogratulate you because you know to convert hard things into easy ones, so again thank you very much bro.

[@calistavicente-bradley4739]

You're the only one I understanx! Congrats ur the best math tutor in KZbin

[@kristy1135]

I appreciate this video. You explain it easily and understandably, your sketches are perfect, and your handwriting isn’t as crappy as every other math teacher 😸. Please keep it up. My trig class is testing my limits this semester! KZbin teachers are angels. Lord give this man health!

[@TheRealDedi]

I was struggling all week in my trig class. These videos have helped me alot thanks for posting!

[@OoTFanboy]

Thanks Patrick, this really helps me and my teacher's not teaching our class very well right now.

[@brando6323]

Freak I’m so scared for my math test tomorrow but this helped me with identities so I actually understand them all now, thank you so much

[@danimoosakhan]

i have quiz tomorrow on this. u are the best teacher i have ever learn from.

[@paddleout639]

Patrick JMT, you are awesome. Thank you so much for awakening my love of math. I had always simply memorized math. Now that I understand it, I LOVE IT! Thank you so so much!!

[@thehrchannel8983]

I just want to say thank you for taking the time to explain all this! You've made my life so much easier.

[@sagala40]

Patrick, your notes are so neat, simple and easy to follow. You are very easy to follow. Thanks for just keeping it simple.

[@melancholicdreamer1189]

Patrick! You're a lifesaver man! Thank you so much! I have the math test tmrw and all I can do is watch videos on the internet to get "sum"thing in my brain!

[@MoTown434]

Here I am in calc 2, running back to this video after learning (the hard way) how imperative it is to know these and recognize them. Thanks patrickJMT!

[@swat6591]

Sec(x)=1/cos(x) because if you see-can't you can't sin (sign language). This was something I made up that has always helped.

[@newbinha2]

He teaches so well and throughly....

[@cilva7able]

When I was learning trigonometric Identities I always wondered what the purpose was. Then when I started taking calculus and doing trigonometric limits, that's when I realized it was very important!

[@kevinfarlinger2799]

Thanks for your help! I've been trying to get these down for the past couple of days. "Sine is sumthing that switches" is really going to help me at test time.

[@maceyh9954]

In 4 minutes and a half of this video, I learnt all I need! Thanks!

[@ryanmurphy7398]

the first 4 minutes of this video has already explained it better than my honors math teacher did in 2 weeks.

[@doktorquack5460]

Oh man! Thank you! I am studying for midterms in my pre-calc class and you have helped a lot so far!

[@deDEbEaSt]

Thank you! My teacher doesn't explain it as well as you. You really saved me from failing the test!

[@kellydicky872]

OH MY GOD I FINALLY UNDERSTAND. YOU'RE A LIFE SAVER AND JUST SAVED MY TRIG GRADE!!!!

[@faust666desrosiers]

This dude is heaven sent.

[@BloodCrystal19]

if only our professor were as good and as clear as you.. then this would be a perfect world. thank you so much. :))

[@sarahguney]

I fell in love with math after i started watching your videos. So grateful. a big THANK YOU!

[@scsoc]

Clear explanation, constructed from basic principals. These relationships are difficult to see unless an explanation, such as yours, shows how another individual understands it. Textbooks nor teachers do this type of explanation on how they leaned and understood a concept. Thank you sir

[@henik9]

Wow I was looking for a way to memorize these more easily. You read my mind, thanks!

[@tradingarmor5562]

This so great! I hate just arbitrarily memorizing stuff but when you know how to derive things, you don't have to!

[@MrAmjustbeautifulme]

only God knows why my teacher doesn't explain us the same way but thanks a lot man you are such a lifesaver xxx

[@SuperLEGION1000]

Best math channel :3

[@patrickjmt]

thanks!

[@mtchll2500]

I don't think so.

[@phpstorm6884]

5:09 "So I'm just drawing some raaandom graphs here..." *draws a pitchfork.* I'll have to watch this video in reverse when I'm done.

[@evelinalaurent1463]

ladies and gentleman, this is how to pay your taxes

[@prateekgurjar1651]

Calculus does help you, you can learn paying taxes anytime man. Overused meme -_-

[@prateekgurjar1651]

Calculus does help you, you can learn paying taxes anytime man. Overused meme -_-

[@Mister_Soyuz_on_YT]

Evelina Laurent May I ask what book title and edition did you had to learn about paying taxes? I want to know in my own. .

[@aniketaniket897]

Plzzz speak in hindi

[@JCWClips]

Well this is one weird thread.

[@JaneDoe-je7nh]

I can see clearly noow the rain has gone!

[@ashwinram472]

OMFG Trignometry is all about understanding to use them in life.But my goddamn Maths teacher just writes these identities and makes all the students as robots mugging up studies.I want to become a intelligent human and not a robot and you showed me the way Hats of to you work.

[@hajdukfamily3281]

an easy way to remember is cosec, sec, cot use the third letter in each and that is what they correspond to. coSec so SIN, seC so COS, and coT so TAN. Hope this helps

[@mcohen2027]

This was really helpful. I like your pace and tone. Thank you for creating the video

[@bsavvy5450]

you explain everything relevant that needs to be known to understand this and it was very helpful thanks.

[@RyusukePrudence]

You helped me do very well in my CAL 1 class, so now my buddies and I are going to continue using your videos for CAL 2

[@haloicon1]

This literally gave really good information. Learn everything I had trouble on. Was simple and easy to follow.

[@inadaizz]

Glad to see so many views Thanks for the upload! I can't help but admire people who help make the world a smarter place free of charge. ♥

[@anishgajera]

This is it, this is the video that I wish I had known about when I was in pre-cal last year. Now I'm in calculus and I need this for the trig derivatives and it is a major help.

[@patrickjmt]

glad it helped you out a bit :)

[@ArushShangari]

Amazing video covering everything in Trigonometry, this has helped me so much!!!!

[@autumnhart508]

Omygoodness, thank you! my teacher just gave us a list of them and told us to memorize them... but knowing where they actually come from helps so much! :D

[@jc64333]

Oh my goodness!!!!!!!! You are amazing! Thank you so much for your help!

[@cheetahpiper6422]

Finally, something in Trig. that actually makes sense!

[@igrieger]

You are good at explaining that. Some teatchers get too confusing when explaining it.

[@DutchKid121]

You're a hero, thank you so much.:)

[@patrickjmt]

DutchKid121 super happy to help :)

[@novetheresegundan2775]

+patrickJMT how do you know what will you divide uhm like divide it by cos or sin

[@the_golden_one4733]

+Novee Therese Gundan yea i have that question in mind too , i guess its just sth to remember . Theres a reason for the answers to the divisions but they r unimportant

[@arcos0255]

So how's you're test?

[@ssonilalit6300]

tqs

[@yucky1336]

patrick i was wondering how you record your videos man. theyre amazing. i feel like i'm watching myself doing the work which is why i think your videos are so sucessfull

[@TheLeontheking]

Really valuable! I encourage everyone to go through the derivations of each of them yourselves - this will activate so much more neurons in your brain, an will be much more fun than just trying to pigheadedly memorize them..

[@patrickjmt]

i agree, but few people do that :)

[@pratiksaha2592]

thank u so much sir i dont think ill ever forget these trig. formulas YOU REALLY ROCKED

[@enkephalin07]

Thanks, this is something I frequently need to reinforce by working it out manually.

[@Fullitaboli]

In Australia we write your csc as cosec and that way it helps us remember the inverse trigs. e.g. the inverse of cot is tan and the trick to it is to look at the third letter in the word and whatever it starts with, that is what the normal trig is. So with sec, the third letter is c so the inverse of sec is cos. With cosec, the third leter is s so the inverse is sin. Hope this helps your confusion.

[@arshiar2822]

wonderfully explained, I feel more confident about my midterm university tomorrow Thanks

[@pritykumaribhagat4031]

Good bro ...I like the way you've used minimum resources without any galm ups...it does the job! God bless you..

[@Marie-ee2kd]

I watched 2 videos prior to this one and felt hopeless... now I actually am beginning to understand this gibberish 😅😅😅 thank you!!!

[@patrickjmt]

come back any time :)

[@abdullahiahmed3429]

I learnt more from you. than my lecturer...thanks matr

[@hans6314]

SOOOOOO WELL SUMMARIZED, EARNED YOU ANOTHER SUBSCRIBER!

[@swatsfab2559]

Woah!! Its the first time i realized math cud be fun!!! Thanku... Hoping 4 more tricks!!

[@dc1727]

You made this video so long ago, but it's helping me so much! Thank you!

[@mckfjfkmcjmf918]

you are the best i am very weak in math but ilearn from you and i feel that math is not bad espacily trignometry it needs little bit effort now i am fully prepared for my test May Allah bless you i love your method of teaching thank you

[@jayantipatel2893]

i can watch your trignometry videos and can prepare for the upcoming exam thanks a lot patrickJMT

[@wblack86]

As always, you were great. Can't thank you enough for taking your personal time to do this for us struggling math students. You rock. PS - Your accent makes me believe you're from PA...or maybe MD. Am I right?

[@patrickjmt]

i grew up in the middle of nowhere in KY, near the Ohio River, across from Indiana. we like put r's in words were they don't belong. such as: warsh your hands with soap, where is the pillar for my bed? etc.

[@Joe-pe8fe]

Couldn't understand anything all these years! Finally understood it in 13 minutes 😂

[@anderss8105]

Hi Patric, iv just donated a few dollars. i really hope more people do the same. Thank you for the enthusiasm and effort you put into these clips! i find very handy when i repeat "old stuff", with my base knowledge and your pedagogic way of teaching im back on tracks in no time. Btw will make a real donation after im done with my studies at the university /Best regards Anders

[@4rrow740]

I loved the way u explained it , trignometry just got a bit easier for me now I suppose and using functions to relate with that just made it whole lot better you helped me and earned a subscriber too ;)

[@patrickjmt]

glad i could help you :)

[@tmax534]

Great Video I am so bad at math and you explained this so well for me im confident about taking my final now

[@gotreflexesprod]

sooo my math teacher is left handed and she has the most beautiful handwriting, and I'm glad you are not giving lefties a bad wrap either

[@youbuusta]

WHY YEARS AFTER TAKING TRIG DOES THIS MAKE SO MUCH SENSE NOW!!!!!!😭

[@adithyanarayanan467]

That was a fantastic video, accompanied by a lucid explanation!

[@scottomakholwa8643]

You so good with identities, i have learnt alot from yah, very awesome!

[@ZzromhackzZ]

I'm preparing for next year's AIME and Waterloo contests and this really helped!

[@dilekozgun2434]

Hmm what a beautiful channel... Thank you from Turkey.

[@moyoceillee684]

This is really good . Excellent sir . You opened my eyes , now I can do it well

[@patrickjmt]

Great 👍

[@doctorlaughtor9884]

Since, Sin=Per/Hyp Cos=Base/Hyp Tan=Per/Base How i remember them is through the phrase, Some People Have Curly Brown Hair Through Proper Brushing The 1st letter of each corresponds to the first letter of the formulae Hope this helped 😊

[@Anasition]

You are a saint , sir . God bless you

[@JShred85]

Thank you Patrick, you are a truly awesome dude!

[@lamwlgabriel]

To remember the anti derivatives, i suggest using the 3rd letter of each name to find out the root co (s) ec is 1/sine se (c) ant is 1/cosine co (t) angent is 1/tangent

[@100equus]

Great visual with excellent handwriting with black pen.