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

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  • Опубликовано: 16 янв 2025

Комментарии • 593

  • @patrickjmt
    @patrickjmt  5 лет назад +60

    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
      @harsathabinav.m 5 лет назад

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

    • @free-energy-systems
      @free-energy-systems 4 года назад

      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
      @dattatraybade9929 2 года назад

      .

    • @ahmadfaisal4820
      @ahmadfaisal4820 2 года назад

      What is key word for memorize these trigonometric identities?

  • @Woutouber222
    @Woutouber222 11 лет назад +513

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

    • @Alex-su9nz
      @Alex-su9nz 9 лет назад +3

      yeah exactly!!!

    • @Xilosphere
      @Xilosphere 9 лет назад +7

      robbybaby1200 Fewer distractions?

    • @iankim748
      @iankim748 8 лет назад +15

      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
      @violiningss 7 лет назад +3

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

    • @OpnWrldgmng
      @OpnWrldgmng 5 лет назад

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

  • @RavenCelestia
    @RavenCelestia 8 лет назад +499

    got an exam on monday, im looking for miracles

    • @justinlewtp
      @justinlewtp 8 лет назад +93

      who needs miracles when u have Patrick

    • @dramawind
      @dramawind 8 лет назад +46

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

    • @coolbeans3138
      @coolbeans3138 7 лет назад +2

      Raven Celestia SAME

    • @rozikhan2744
      @rozikhan2744 7 лет назад +32

      got an exam in 20 mins I need jesus 🙌

    • @dustinsimmons4418
      @dustinsimmons4418 7 лет назад +5

      how did yall do?

  • @TheCatMasterOfKnow
    @TheCatMasterOfKnow 8 лет назад +159

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

    • @patrickjmt
      @patrickjmt  8 лет назад +57

      +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
      @PimpMatt0 8 лет назад +12

      I lose my patience every year I go in math.

    • @rozikhan2744
      @rozikhan2744 7 лет назад +4

      Try physics 😥

    • @Whaddif_
      @Whaddif_ 5 лет назад +8

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

    • @bootseen344
      @bootseen344 5 лет назад

      @@Whaddif_ so fucking true

  • @princessdiana2414
    @princessdiana2414 9 лет назад +34

    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
      @RawDoggin_78 3 года назад +4

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

  • @neootukile208
    @neootukile208 11 лет назад +65

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

  • @juanvolvoturbo
    @juanvolvoturbo 8 лет назад +559

    Calculus makes me feel like a failure in life.

    • @chris-dd6uq
      @chris-dd6uq 8 лет назад +55

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

    • @robertwilsoniii2048
      @robertwilsoniii2048 7 лет назад +59

      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
      @birdobonkers5205 6 лет назад +17

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

    • @gailykaira
      @gailykaira 6 лет назад +13

      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
      @palootto4021 6 лет назад +4

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

  • @MP-wb7sh
    @MP-wb7sh 8 лет назад +45

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

  • @bryantiu1151
    @bryantiu1151 11 лет назад +336

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

  • @hurrdurr25
    @hurrdurr25 9 лет назад +124

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

    • @daple1997
      @daple1997 9 лет назад +10

      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
      @prophetic1012 8 лет назад +1

      Just shut up and HOLD THE DOOR!

    • @robertwilsoniii2048
      @robertwilsoniii2048 7 лет назад +8

      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
      @versus13 5 лет назад

      Dustine smith HODORRRRR HODORRR

  • @A_C2215
    @A_C2215 9 лет назад +8

    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 :)

  • @RyuHaruse
    @RyuHaruse 11 лет назад +4

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

  • @evelinalaurent1463
    @evelinalaurent1463 9 лет назад +110

    ladies and gentleman, this is how to pay your taxes

    • @prateekgurjar1651
      @prateekgurjar1651 8 лет назад +3

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

    • @prateekgurjar1651
      @prateekgurjar1651 8 лет назад

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

    • @Mister_Soyuz_on_YT
      @Mister_Soyuz_on_YT 8 лет назад

      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
      @aniketaniket897 8 лет назад

      Plzzz speak in hindi

    • @JCWClips
      @JCWClips 5 лет назад +2

      Well this is one weird thread.

  • @SupremeFallenX
    @SupremeFallenX 9 лет назад +22

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

  • @nursyazreenmahdzir3597
    @nursyazreenmahdzir3597 9 лет назад +3

    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 !

  • @hniang2
    @hniang2 11 лет назад +11

    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
      @patrickjmt  11 лет назад +3

      thanks for such kind words, i appreciate them ;)

  • @Hardstyle_Queen
    @Hardstyle_Queen 8 лет назад +22

    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
      @patrickjmt  8 лет назад +6

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

    • @Xxpussydestroyerxx12
      @Xxpussydestroyerxx12 8 лет назад

      小林雪羽

  • @RexGalilae
    @RexGalilae 10 лет назад +1

    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!!

  • @OoTFanboy
    @OoTFanboy 13 лет назад +1

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

  • @phpstorm6884
    @phpstorm6884 9 лет назад +6

    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.

  • @newbinha2
    @newbinha2 14 лет назад +1

    He teaches so well and throughly....

  • @AsteruxGaming
    @AsteruxGaming 10 лет назад +1

    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
    @Brownie4078 8 лет назад +1

    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!!!

  • @TheRealDedi
    @TheRealDedi 12 лет назад +1

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

  • @patrickjmt
    @patrickjmt  14 лет назад +2

    @MIT2004 anything in particular?

  • @cmhammo2025
    @cmhammo2025 8 лет назад +1

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

  • @kaileykeenan3018
    @kaileykeenan3018 10 лет назад +1

    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

  • @alaakhalid96
    @alaakhalid96 10 лет назад +1

    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!

  • @faust666desrosiers
    @faust666desrosiers 7 лет назад +2

    This dude is heaven sent.

  • @doktorquack5460
    @doktorquack5460 12 лет назад +1

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

  • @JaneDoe-je7nh
    @JaneDoe-je7nh 9 лет назад +26

    I can see clearly noow the rain has gone!

  • @calistavicente-bradley4739
    @calistavicente-bradley4739 5 лет назад

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

  • @DutchKid121
    @DutchKid121 9 лет назад +47

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

    • @patrickjmt
      @patrickjmt  9 лет назад +10

      DutchKid121 super happy to help :)

    • @novetheresegundan2775
      @novetheresegundan2775 9 лет назад

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

    • @the_golden_one4733
      @the_golden_one4733 9 лет назад

      +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
      @arcos0255 6 лет назад

      So how's you're test?

    • @ssonilalit6300
      @ssonilalit6300 6 лет назад

      tqs

  • @henik9
    @henik9 14 лет назад +1

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

  • @danimoosakhan
    @danimoosakhan 9 лет назад +2

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

  • @jc64333
    @jc64333 10 лет назад +1

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

  • @sagala40
    @sagala40 11 лет назад

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

  • @paddleout639
    @paddleout639 10 лет назад +1

    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!!

  • @ryanmurphy7398
    @ryanmurphy7398 11 лет назад

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

  • @kevinfarlinger2799
    @kevinfarlinger2799 9 лет назад +1

    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.

  • @brando6323
    @brando6323 5 лет назад +2

    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

  • @thehrchannel8983
    @thehrchannel8983 10 лет назад +1

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

  • @swat6591
    @swat6591 9 лет назад +9

    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.

  • @BloodCrystal19
    @BloodCrystal19 12 лет назад

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

  • @rianshabani9181
    @rianshabani9181 4 года назад

    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.

  • @MoTown434
    @MoTown434 7 лет назад +1

    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!

  • @cilva7able
    @cilva7able 8 лет назад +1

    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!

  • @maceyh9954
    @maceyh9954 4 года назад

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

  • @deDEbEaSt
    @deDEbEaSt 10 лет назад +1

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

  • @ashwinram472
    @ashwinram472 11 лет назад

    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.

  • @mcohen2027
    @mcohen2027 9 лет назад +1

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

  • @kristy1135
    @kristy1135 5 лет назад

    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!
    RUclips teachers are angels.
    Lord give this man health!

  • @mackaseck6638
    @mackaseck6638 9 лет назад +3

    sir, you deserve a cookie but since the price of cookies is off the roof, i hope you settle for a THANK YOU

    • @patrickjmt
      @patrickjmt  9 лет назад +8

      When did the price of cookies get so expensive?

  • @cheetahpiper6422
    @cheetahpiper6422 5 лет назад +1

    Finally, something in Trig. that actually makes sense!

  • @kellydicky872
    @kellydicky872 10 лет назад

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

  • @yucky1336
    @yucky1336 14 лет назад

    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

  • @SuperLEGION1000
    @SuperLEGION1000 10 лет назад +86

    Best math channel :3

  • @melancholicdreamer1189
    @melancholicdreamer1189 7 лет назад

    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!

  • @scsoc
    @scsoc 9 лет назад

    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

  • @MrAmjustbeautifulme
    @MrAmjustbeautifulme 10 лет назад +19

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

  • @wblack86
    @wblack86 11 лет назад +3

    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
      @patrickjmt  11 лет назад +7

      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.

  • @tradingarmor5562
    @tradingarmor5562 7 лет назад

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

  • @enkephalin07
    @enkephalin07 2 года назад +1

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

  • @JShred85
    @JShred85 12 лет назад

    Thank you Patrick, you are a truly awesome dude!

  • @hans6314
    @hans6314 2 года назад

    SOOOOOO WELL SUMMARIZED, EARNED YOU ANOTHER SUBSCRIBER!

  • @hajdukfamily3281
    @hajdukfamily3281 3 года назад +2

    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

  • @TheZakev
    @TheZakev 9 лет назад +1

    You're the man, bro :) Thank you.

  • @pratiksaha2592
    @pratiksaha2592 8 лет назад +1

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

  • @EriAirlangga
    @EriAirlangga 6 лет назад +6

    I'm watching this after I took my exam 30 years ago

  • @ArushShangari
    @ArushShangari Год назад

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

  • @sarahguney
    @sarahguney 11 лет назад

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

  • @Anasition
    @Anasition 11 лет назад

    You are a saint , sir . God bless you

  • @bsavvy5450
    @bsavvy5450 8 лет назад

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

  • @Fullitaboli
    @Fullitaboli 12 лет назад

    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.

  • @abdullahiahmed3429
    @abdullahiahmed3429 9 лет назад

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

  • @yuventures9620
    @yuventures9620 7 лет назад

    love this vid. It helps a lot. Thanks Patrick!

  • @anderss8105
    @anderss8105 11 лет назад

    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

  • @haloicon1
    @haloicon1 7 лет назад

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

  • @Dolovely
    @Dolovely 10 лет назад +1

    Thank you!! This was extremely helpful :)

  • @gotreflexesprod
    @gotreflexesprod 12 лет назад

    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

  • @dilekozgun2434
    @dilekozgun2434 5 лет назад +1

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

  • @pinkmuffinparis07
    @pinkmuffinparis07 12 лет назад +1

    you are amazing :P) thank you so much!

  • @gannaeatu
    @gannaeatu 12 лет назад +1

    This is great. Really. Keep it up

  • @ruggjess
    @ruggjess 12 лет назад +1

    Perfect! Thank you!!

  • @RyusukePrudence
    @RyusukePrudence 9 лет назад

    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

  • @dc1727
    @dc1727 7 лет назад

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

  • @bigdream9619
    @bigdream9619 8 лет назад

    i love you the best teacher ever

  • @sohoyankee66
    @sohoyankee66 10 лет назад

    This is amazing. Thanks a bunch, Patrick.

  • @angelahurtado2328
    @angelahurtado2328 10 лет назад

    Thank you so much for all your great help!

  • @jwanbass
    @jwanbass 11 лет назад

    this is awesome! its like night and day! thanks

  • @adithyanarayanan467
    @adithyanarayanan467 4 года назад

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

  • @inadaizz
    @inadaizz 8 лет назад

    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. ♥

  • @igrieger
    @igrieger 7 лет назад

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

  • @100equus
    @100equus 12 лет назад

    Great visual with excellent handwriting with black pen.

  • @anishgajera
    @anishgajera 4 года назад

    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
      @patrickjmt  4 года назад

      glad it helped you out a bit :)

  • @autumnhart508
    @autumnhart508 9 лет назад

    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

  • @scottomakholwa8643
    @scottomakholwa8643 7 лет назад

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

  • @magranin7319
    @magranin7319 4 года назад

    The best refresher ever

  • @jayantipatel2893
    @jayantipatel2893 9 лет назад

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

  • @lindsliz174
    @lindsliz174 7 лет назад

    Dude. You are my hero.