Proving the Double and Half Angle Formulas for Trigonometry (Precalculus - Trigonometry 27)

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  • Опубліковано 10 гру 2024

КОМЕНТАРІ • 49

  • @robs7527
    @robs7527 3 роки тому +100

    Mr. Leonard! I am a former student from your Calc 2 class at MJC! Hope all is well! I finished my engineering degree and I’m so thankful to have participated in your lectures.

  • @abednoueiry8759
    @abednoueiry8759 3 роки тому +54

    Professor, I'm not really sure if you'll read this but I thought I needed to leave this comment here either way. Around 2 years ago, I found a field I'm really passionate about, but I unfortunately did not have the mathematical chops to deal with its rigor. Math was always a subject that I was terrified of thinking I'm not smart enough to succeed in, but to be honest, that was 100% down to bad teaching methods and me not putting enough work in. Fast forward those 2 years, having gone through all your playlists from pre-algebra to Calc 3, I've passed all my foundational classes with straight A's, and I'm now at a well-respected university doing the degree I've always wanted to do.
    Even though you've never taught me in person, I can't stress on the impact you've had on my academic career so far. You are a truly phenomenal teacher, and I sincerely hope your students appreciate how lucky they are to have you. I don't really know what to say at this point other than thank you! Keep being awesome!

  • @drewmareburger3798
    @drewmareburger3798 3 роки тому +23

    Professor Leonard looks even more like a beast now than from all his old Calc UA-cam videos I watch. Good work

  • @fritz6600
    @fritz6600 3 роки тому +8

    The guy single handedly saving lives and saving mathematics at the same time. Bless you Professor. Thank you for your service to humanity.

  • @s_1872
    @s_1872 3 роки тому +7

    Prof! I have taken Calc 1,2,3 you are not only teaching us how to do math and solve problems like other people do, you actually let us understand every single thing behind calculus instead of giving us methods to solve for certain cases like other teachers do. Please if you read this, I want you to know that you gave me hope to continuo perusing my major . you are the best:) !

  • @irvlazaro7302
    @irvlazaro7302 3 роки тому +5

    I started in Late August on your Stats playlist, then went to your intermediate Algebra and now about to finish your Pre-Calc Playlist. I'm now ready for your Calculus 1,2,3 playlists, thank your for making me enjoy math again.

  • @mattdodgers9533
    @mattdodgers9533 2 роки тому +1

    Professor Leonard is the best math teacher I have ever had the pleasure to learn from. He is thorough, patient, and inspirational. He always reminds us that we can do it. And we can because he gives us the tools.

  • @jamesgrey3320
    @jamesgrey3320 3 роки тому +2

    in france we don't have professor looking like clark kent ! i must say that i envoy looking at his video because this man is very clear in explaining maths, he's a very good teacher and makes math easy to anderstand and sympatic i thank you professor for your generosity from france !

  • @edgarcanela3155
    @edgarcanela3155 3 роки тому +3

    I know I am a little late, but congrats on surpassing half a million subscribers! Your calculus videos got me through my first two years of math, and I want to you know that I am really grateful for that. Wishing you and your family all the best professor Leonard! Stay safe and God bless.

  • @mrboyban
    @mrboyban 3 місяці тому

    What a legend! The builder's community must be very proud to have such a clever member amongst them.

  • @garass2700
    @garass2700 3 роки тому +3

    Honestly I passed calculus 1 and2 because of you.and now differential equations.thanks a lot I wish you good health you and your family

  • @georgesadler7830
    @georgesadler7830 2 роки тому +1

    Professor Leonard ,thank you for another tremendous video/lecture on Proving the Double and Half Angle Formulas in Trigonometry/Precalculus. I used these well known formulas in Calculus and Electrical Engineering courses in years past and they are very useful in solving complex problems. Proving formulas and concepts in Mathematics are also important.

  • @soun-jawalters1773
    @soun-jawalters1773 11 місяців тому +1

    This video is very clear. Much appreciated.

  • @adrianhanson5283
    @adrianhanson5283 3 роки тому +6

    I'm crossing my fingers that linear algebra will start up by the time I take it next quarter! I don't know how to pass a math class without your videos anymore

  • @CPT_SOLO
    @CPT_SOLO 3 роки тому +2

    So happy I found your channel

  • @roadchewerpe5759
    @roadchewerpe5759 3 роки тому +2

    Thank you for this. I need to learn these to help with calculus.

  • @masternobody1896
    @masternobody1896 3 роки тому +5

    prof is a legend

  • @beesanal-attal5679
    @beesanal-attal5679 3 роки тому +2

    Thank you prof for your amazing work
    I am watching from over the seas ❤️

  • @akvmaths
    @akvmaths 3 роки тому +3

    You are inspiration for us❤️

  • @SummaryPhysics
    @SummaryPhysics Рік тому +1

    Thankyou very much dear sir❤

  • @CPT_SOLO
    @CPT_SOLO 3 роки тому +2

    Your students are the luckiest students ever!!

  • @alikhalidsalim4865
    @alikhalidsalim4865 3 роки тому +2

    Love u prof Lenoard

  • @shovellware
    @shovellware Рік тому +1

    i love this man

  • @olamilekanogunjobi4408
    @olamilekanogunjobi4408 11 місяців тому

    He's explaining so cold..... breaking it into compartment

  • @bolgarang9740
    @bolgarang9740 2 місяці тому

    Thank you so much brother

  • @masternobody1896
    @masternobody1896 3 роки тому +3

    amaazing video

  • @ojingaj30
    @ojingaj30 3 роки тому +2

    BRAVO!!!

  • @spurti
    @spurti 3 роки тому +2

    Hii so could you make a video on how to derive the formula for sum and difference trig identities.

  • @jesusjacobo2451
    @jesusjacobo2451 Рік тому +1

    Damm, is he a math teacher or a super modle 🥵

  • @lalapapa9357
    @lalapapa9357 3 роки тому +2

    In 1 year, I'll be sure to come back to this video after mastering the other lower level mathematics. xD

    • @losrussets8945
      @losrussets8945 3 роки тому +2

      Yeah, I wish I would have found him sooner. I would be having a much better time with calc 3 if I had learned from Leonard the whole time.

  • @terencewright2223
    @terencewright2223 2 місяці тому

    Excellent.

  • @HARSHRAJ-ph6ji
    @HARSHRAJ-ph6ji 3 роки тому +1

    Sir your VIDEOS ARE awesome please make video on JEE ADVANCED IT'S A HUMBLE REQUEST

  • @beesanal-attal5679
    @beesanal-attal5679 3 роки тому +3

    Can anyone suggest a good channel for discrete mathematics ?🙏🏻

    • @HimuraK1
      @HimuraK1 2 роки тому +2

      Would like to know also

  • @cavelinguam6444
    @cavelinguam6444 Рік тому +1

    Awesome

  • @gabrielv2187
    @gabrielv2187 7 місяців тому

    brilliant

  • @Zanebrain101
    @Zanebrain101 2 роки тому

    Prof. Leonard, do you have a lifting social media?

    • @Zanebrain101
      @Zanebrain101 2 роки тому

      you should consider making a joint account.

  • @xiiixiiih.16
    @xiiixiiih.16 2 роки тому

    🍎I don't under stand ?
    I'm not good in math.🙄

  • @aamna_0626
    @aamna_0626 3 роки тому

    ...

  • @hunterx2501
    @hunterx2501 Рік тому

    Why am i getting teen wolf vibes

  • @AlfredPhiri-b9e
    @AlfredPhiri-b9e 3 місяці тому

    you've saved my a** sir.🥲