Calculus I - Derivatives of Sine and Cosine Functions - Proofs

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  • เผยแพร่เมื่อ 20 ม.ค. 2025

ความคิดเห็น • 62

  • @mwanziesaffa4167
    @mwanziesaffa4167 ปีที่แล้ว +1

    I'm older - middle-aged and the way I learned we were taught to use a delta x instead of h, but no worries I understood every step because you've got a KNACK for teaching. Thank you, sir, whoever you are.

  • @thuggishhoudini5881
    @thuggishhoudini5881 10 ปีที่แล้ว +11

    Thank you! Finally someone who explains it properly.

  • @aasthaarunika4848
    @aasthaarunika4848 5 ปีที่แล้ว +7

    You explain very nicely in an easy way, sir!
    I really liked your video, I could understand the topic very easily...
    Thank you...😊✌

  • @abdulhalim520
    @abdulhalim520 10 ปีที่แล้ว +7

    I have done very, very well in my exams, just following your videos, although I do not have to learn the proofs, it gives me a much better understanding of what's going on, so it's fundamental to learn this.

    • @coffeebirdtree
      @coffeebirdtree 7 ปีที่แล้ว +7

      personally i can't bring myself just to memorize formulas without understanding why they work

    • @guacamole3109
      @guacamole3109 6 ปีที่แล้ว +2

      coffeebirdtree same bro same

  • @jacintakiema3472
    @jacintakiema3472 6 ปีที่แล้ว +2

    Best teacher ever ,God bless you

  • @narayanpareek7593
    @narayanpareek7593 4 ปีที่แล้ว

    Sir i am from india but sir you teach so much better than indian youtube teaching channels

  • @victorrivera1606
    @victorrivera1606 2 ปีที่แล้ว

    This is beautiful! I hate when we are given formulas without telling how they arrive. Thank you! I study math on my own for hobby.

  • @lindamtshali6
    @lindamtshali6 9 ปีที่แล้ว +35

    i think you should lecture my lecturer...

  • @finnaddict
    @finnaddict 8 ปีที่แล้ว

    Fantastic video mate :) Thank you for showing this so clearly, and for taking the time to do both :)

  • @saleemmalikk1223
    @saleemmalikk1223 6 ปีที่แล้ว

    After all i found it thank u very very much this was an incresible piece of work

  • @felixcopra3910
    @felixcopra3910 5 ปีที่แล้ว

    O how i wish i could personally thank you sir.. Thank you for this most informative proving for the derivative of sin x and cos x

  • @hansrajsingh3517
    @hansrajsingh3517 3 ปีที่แล้ว

    U made it much simpler 🙌🙌

  • @muhammadasim9218
    @muhammadasim9218 7 ปีที่แล้ว +2

    sir very satisfactory explanation thank you

  • @mimishuu3130
    @mimishuu3130 6 ปีที่แล้ว +4

    thank you for this. really helpful.

  • @cebukid70
    @cebukid70 3 ปีที่แล้ว

    I would have gotten an A in Calculus 1 if this lecture (and TH-cam) was available back in my day (I took Calculus 1 in 1989)

  • @futuring2024
    @futuring2024 11 ปีที่แล้ว

    Thank you for your help !!! I finally could finish my homework !!!! thanks :)

  • @gottadomor7438
    @gottadomor7438 3 ปีที่แล้ว

    T/y/v/m for this mathematical explanation of why the derivative of sinx is cosx.
    I've seen a YT defining it graphically but still can't absorb that method; this one tho does :make sense. And hopeful it will now ease along "seeing" the graphical proof. T/y again.

  • @varadvithalkj1716
    @varadvithalkj1716 8 ปีที่แล้ว +2

    u r the undisputed champion

  • @susannaa2021
    @susannaa2021 4 ปีที่แล้ว

    Your the great master keep it up

  • @deimaphikharsati6080
    @deimaphikharsati6080 4 ปีที่แล้ว +1

    Thank you sir for this explanation

  • @sayedsadiibrahimi6729
    @sayedsadiibrahimi6729 6 ปีที่แล้ว +1

    Thanks for helping us with providing of this video .

  • @mariapersaud9685
    @mariapersaud9685 7 ปีที่แล้ว

    YOU JUST SAVED MY LIFE

  • @DanielGuiler
    @DanielGuiler 8 ปีที่แล้ว +1

    Awesome video

  • @HaMza-cp9yc
    @HaMza-cp9yc 6 ปีที่แล้ว

    How i get derivatives of complex trigonometric equation

  • @shaunkirk6048
    @shaunkirk6048 7 ปีที่แล้ว +1

    Can you explain how we turn the limit of X+ H into the angle addition formula when proving the derivative of cosine = - sine and sine = cosine? I find the formula for Sum to Product easier to use as it makes more sense when say cosine - cosine and we use the Sum to Product formula

    • @TheInfiniteLooper
      @TheInfiniteLooper  7 ปีที่แล้ว

      Shaun Kirk the video explains how we do that. Did you have a specific question on one of the steps? The sum to product formula applied to sin(x+h) - sin(x) and same for cosine also works and may even be a bit simpler. Didn't occur to me at the time because it's a less commonly used family of formulas in my experience.

  • @sleverlight
    @sleverlight 5 ปีที่แล้ว

    14:10 how is sinh/h=1?????

    • @TheInfiniteLooper
      @TheInfiniteLooper  5 ปีที่แล้ว

      It's not. The limit of that as h goes to 0 is 1. I have a video that explains that, called "special trig limits proof 1"

    • @sleverlight
      @sleverlight 5 ปีที่แล้ว

      @@TheInfiniteLooper K thanks I'll check it out

  • @tenton2000k
    @tenton2000k 8 ปีที่แล้ว +6

    Did you learn all of this from your professors at UPenn? Or did you have to study on your own?

    • @TheInfiniteLooper
      @TheInfiniteLooper  8 ปีที่แล้ว +6

      This was all before Penn. I finished Calc 3 before going there.

  • @ralfbodemann1542
    @ralfbodemann1542 7 ปีที่แล้ว +1

    Could you please link to the video where you actually proove that the limit as x goes to zero of (1-cosx)/x equals zero?
    It's easy if you use the Taylor series of cos(x). But what, if you start from the scratch?

  • @عمارالقحطاني-ق5ن
    @عمارالقحطاني-ق5ن 8 ปีที่แล้ว

    thank you my best techaer

  • @jokatech1
    @jokatech1 6 ปีที่แล้ว

    very helpful man. thanks

  • @zakiahr7379
    @zakiahr7379 5 ปีที่แล้ว

    you are amazing !!!!!!

  • @kapili-pili1339
    @kapili-pili1339 8 ปีที่แล้ว

    thanks verrrrrrrry much...ts all clear now!!!

  • @ianmoseley9910
    @ianmoseley9910 4 ปีที่แล้ว +1

    link to the proof of the limits would be helpful

    • @thatmathkid-anthony6658
      @thatmathkid-anthony6658 4 ปีที่แล้ว

      This is a very good video. I have the proofs here. th-cam.com/video/64dguvQBwUQ/w-d-xo.html

  • @zelda64rules
    @zelda64rules 7 ปีที่แล้ว

    And from that basis, you can get the derivatives of the other 4 expressions (tanx, cscx, secx, and cotx)

  • @NOTHING-po9re
    @NOTHING-po9re 5 ปีที่แล้ว +1

    Thank you

  • @mohamedarwah600
    @mohamedarwah600 8 หลายเดือนก่อน

    Thank you very much

  • @sabahatali8547
    @sabahatali8547 6 ปีที่แล้ว

    plz tell me how cosh-1/h =0
    because 0/0 is not zero

    • @TheInfiniteLooper
      @TheInfiniteLooper  6 ปีที่แล้ว +1

      I have a separate video explaining why that limit is zero. Search special trig limits on my channel, it should be one of the first few results.

    • @robertveith6383
      @robertveith6383 2 ปีที่แล้ว

      Your numerator is missing grouping symbols.

  • @yahyabarwari412
    @yahyabarwari412 8 ปีที่แล้ว +1

    Thanks a lot .... .

  • @akhikhondokarpriya8279
    @akhikhondokarpriya8279 5 ปีที่แล้ว

    Thanks

  • @onepunchkatz6789
    @onepunchkatz6789 7 ปีที่แล้ว

    THANK YOU

  • @KellWhitlock
    @KellWhitlock 7 ปีที่แล้ว +3

    Math is fucking beautiful.

    • @robertveith6383
      @robertveith6383 2 ปีที่แล้ว

      Stop your major cursing. It is ignorant and needless, especially on a mathematics forum.

  • @RR_Sathua
    @RR_Sathua 4 ปีที่แล้ว

    Sir tan function ka proof please😫🙏🙏💓😫🙏🙏💓🙏🙏🙏

  • @87我是-h3u
    @87我是-h3u 7 ปีที่แล้ว

    d/dx(cosx)
    =d/dx(sin(pi/2-x)
    Use chain rule and you will get
    =-(cos(pi/2-x))
    =-sinx

  • @KULDEEPSINGH-rh3go
    @KULDEEPSINGH-rh3go 8 ปีที่แล้ว

    It would be better if you explained it with the help of Graph

  • @anthonytruong1061
    @anthonytruong1061 11 ปีที่แล้ว

    How does (cosh-1)/h equal (1-cosh)/h? Wouldn't it be equal to (-1+cosh)/h instead?

    • @TheInfiniteLooper
      @TheInfiniteLooper  11 ปีที่แล้ว +3

      It's the limits that are equal, not the expressions inside the limits.
      limit as h goes to 0 of [(1 - cos h)/h] = 0
      limit as h goes to 0 of [(cos h - 1)/h] = 0

  • @hello_namoo
    @hello_namoo 7 ปีที่แล้ว

    Can you be my teacher

  • @thomasefternavn9037
    @thomasefternavn9037 6 ปีที่แล้ว

    You could also have said that since h -> 0 and cos(0) = 1 the (cos(h)-1)/h would be 0/h = 0, no multiplying 0 with -1 needed :-) (This was at the end of your proof for sin' )

    • @TheInfiniteLooper
      @TheInfiniteLooper  6 ปีที่แล้ว +1

      Thomas Efternavn no, you can’t do that. If you let h go to 0 in the numerator then you have to do it in the denominator also. And that would give you 0/0 here, which means something else needs to be done.