How To Graph Trigonometric Functions | Trigonometry

This trigonometry video tutorial explains how to graph sine and cosine functions using transformations, horizontal shifts / phase shifts, vertical shifts, amplitude, and the period of the sinusoidal function. This video contains many examples and practice problems on graphing trigonometric functions for you to master this topic.
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The full version explains how to graph secant, cosecant, tangent and cotangent functions.

Пікірлер: 204

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor2 жыл бұрын

    Full 1 Hour 25 Minute Video: www.patreon.com/MathScienceTutor Direct Link to The Full Video: bit.ly/38wtIWU

  • @Rose-zq5xo

    @Rose-zq5xo

    9 ай бұрын

    But why change it to 4 pi over 2 instead of leaving it as 2 pi in the second last question y=sin( x - pi/2)

  • @GeoffreyHill1981
    @GeoffreyHill19813 ай бұрын

    I'm in my early 40s and just started college. You are doing the lord's work.

  • @adityachakraborty9666

    @adityachakraborty9666

    Ай бұрын

    Excellent example of age is just a number

  • @sindilengomane7063

    @sindilengomane7063

    2 күн бұрын

    🎉

  • @auset3475
    @auset34752 жыл бұрын

    You have literally saved me from failing an exam. I am joining your member channel tonight, after work. I have upcoming Calculus, Chemistry, Physics, Org. Chem.classes in the future and I will need your expertise!!!!!!!!!!!!! Thank you for making math less intimidating. You are a gift!!!

  • @tiffaroro4238

    @tiffaroro4238

    2 жыл бұрын

    Hello incase you need help in online classes,assignments and tasks ,I'm here to help you out.

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    @glorihol6803

    2 жыл бұрын

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    @deeepdish

    2 жыл бұрын

    @@tiffaroro4238 no

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    @amnahiba4724

    2 жыл бұрын

    @@tiffaroro4238 hey

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    @tiffaroro4238

    2 жыл бұрын

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  • @tashnimulmazid9706
    @tashnimulmazid9706 Жыл бұрын

    It’s crazy how much better I learn from these videos over my actual classes. I can’t thank you enough!

  • @randommeep
    @randommeep2 жыл бұрын

    I literally learned more here than my lecture-- you are the reason why I am doing so well in my class

  • @yoharn5487

    @yoharn5487

    26 күн бұрын

    FR my lectures are useless

  • @mendozaleonnecaezarl.7525
    @mendozaleonnecaezarl.75254 ай бұрын

    Boutta fail my pre calculus exam 🔥🔥🔥

  • @Tayspeaksfacts

    @Tayspeaksfacts

    Ай бұрын

    How was it?

  • @bnguyen319

    @bnguyen319

    Ай бұрын

    He failed……

  • @SamudraFlavorsYT

    @SamudraFlavorsYT

    15 күн бұрын

    :((

  • @DarkPrincess_M

    @DarkPrincess_M

    11 күн бұрын

    How was the test?

  • @AbhigyanKeshav

    @AbhigyanKeshav

    8 күн бұрын

    What is Andrew tate start teaching calculus

  • @georgesadler7830
    @georgesadler78302 жыл бұрын

    MR. Organic Chemistry Tutor, thank you for showing high school and college students How to Graph Trigonometric Functions the correct way. You are the first instructor that showed me How to Graph Trigonometric Functions the correct way.

  • @evanwalsh8808
    @evanwalsh88082 жыл бұрын

    Tutors at my school couldn't teach me this in over two hours what this video accomplished in 20 mins... thank you sir and thank god for KZread tutorials.

  • @victoriar8928
    @victoriar8928 Жыл бұрын

    this was explained perfectly, I was so stressed bc during lectures I did not understand what was going on. you went over basics and it helped so much!!

  • @user-rz6bu8jh1y
    @user-rz6bu8jh1y2 жыл бұрын

    I am Iraqi. I loved your method of teaching. It is wonderful. Thank you. You solved me a lot of problems in mathematics. I no longer suffer from functions. Thank you دفعه ٢٠٢٢

  • @azhym5536

    @azhym5536

    2 жыл бұрын

    Are u Kurdish? lol

  • @yusufaksu4862

    @yusufaksu4862

    11 ай бұрын

    I’Iraqqq tot

  • @Desvis

    @Desvis

    7 ай бұрын

    What does you being Iraqi have to do with the video though

  • @WarmNapkin
    @WarmNapkin2 жыл бұрын

    I love you. I spent two hours in my precalc lecture last wednesday absolutely oblivious, you made this so easy to understand. Thank you so much.

  • @Sconnie1998
    @Sconnie1998 Жыл бұрын

    I am taking a trig course this semester, and I learn more from these videos that I do from my professor or her handouts. This channel teaches me all I need to know to get my assignments done in less time than the lectures or any hand outs/reading!

  • @Bravybrown
    @Bravybrown Жыл бұрын

    First few mins in and I already understood a bit better thanks. My instructor in trig has been doing it for awhile and leaves vital info out during his lecture vids.

  • @seagullz.1019
    @seagullz.10192 ай бұрын

    I have my term final tomorrow and part of it dealt with cosine and sine functions. You are a life saver, I didn't understand this until just now

  • @user-op9rg2vw1n
    @user-op9rg2vw1n3 ай бұрын

    I’m literally speechless of words to praise you of your knowledge+your aptitude of explanation. A real life saver. Are you a human being?

  • @Jmpwfdpdl
    @Jmpwfdpdl24 күн бұрын

    For anyone wondering how he figures out the tick mark values on the x-axis: there are 5 critical points in the sin/cos cycle. Look at a one cycle of a cos/sin graph, and there will be 5 values: 2 values dictating the upper/lower bounds (y-axis values), and 3 values that will cross the x-axis (zeros). In order to find those critical point values (if you're dealing with a phase-shift), you find the value of the phase shift (0=Bx+c, solving for x), and then you add pi/2 recursively. For example, for y=sin(x+pi/3), the graph will start at x=-pi/3. Critical point #1 is -pi/3. To find critical point #2, -pi/3 + pi/2 = pi/6. To find critical point #3, pi/6 + pi/2 = 2pi/3. And so on until you have 5 values. You can use a calculator to add everything to make it easier. if you're still having trouble, google LibreText Mathematics section 2.4 on Phase shift.

  • @suzansuzan1960
    @suzansuzan1960Ай бұрын

    Today I did one of the questions on my exam that had the most points just by watching your video. Thank you very much for helping me and many other students, I can't explain how grateful I am:)

  • @nyeinlach
    @nyeinlach6 ай бұрын

    thank you for sharing your knowledge, i watched this before taking my precalc quiz this morning and i got a 100. this by far is the toughest unit yet and i couldn't have gotten through it w/o your help

  • @Vallerino0
    @Vallerino03 жыл бұрын

    thankyou again for saving my life and my moms voice sir

  • @fjvillas2722
    @fjvillas27222 жыл бұрын

    mr. tutor you are an absolute lifesaver, thank you, I felt like I was gonna tear my hair out when I was trying to answer this

  • @alreeyanmazhar1251
    @alreeyanmazhar12518 ай бұрын

    Your videos are so simple and easy to understand ❤

  • @abdullahshehabeddin1946
    @abdullahshehabeddin19462 жыл бұрын

    This video was so helpful, thank you so much!

  • @SamudraFlavorsYT
    @SamudraFlavorsYT15 күн бұрын

    I love you so much man I could not understand a thing about drawing trig graphs in class. You are amazing

  • @alana2597
    @alana25973 жыл бұрын

    THANK YOU! I literally have a test on this tomorrow you are the best teacher!

  • @ABAMTV12
    @ABAMTV128 ай бұрын

    Spent an hour trying to figure this out based on the book and modules our teacher provided but this video taught me in less than 7 mins

  • @kingtoby9769
    @kingtoby97693 жыл бұрын

    Sir you're the best..... I love you so much ❤️. And wish I could even recognize you 🤧🤧😫 You made me pass my. Exam I failed twice😫😫😭😭

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    @aidt47843 ай бұрын

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  • @_romatomato_
    @_romatomato_ Жыл бұрын

    This helped so much! Thank you!

  • @mikaylasnowdon
    @mikaylasnowdon Жыл бұрын

    thank u, im struggling studying for my midterm and this helps sm

  • @420sushitrashu4
    @420sushitrashu42 ай бұрын

    You're the goat 🐐 better than my maths teacher

  • @michaelaalsukhon5243
    @michaelaalsukhon52432 жыл бұрын

    This helped me so much!! Thank you!

  • @walaaalsheblak5787
    @walaaalsheblak57873 жыл бұрын

    I love your vids helps my dad learn better:)

  • @TheDavidlloydjones

    @TheDavidlloydjones

    3 жыл бұрын

    There's nothing "video" here. The half-wit has entirely missed the opportunity to use a visual medium to show why these trigonometric ratios take the shape they do -- because radii stay th same while the other sides of the triangles involved vary. Just a horrid, stupid, ignorant waste.

  • @L2.Lagrange

    @L2.Lagrange

    3 жыл бұрын

    @@TheDavidlloydjones This is by far the most upset I have seen somebody get from a free trigonometry lesson

  • @lesserknownfacts7849

    @lesserknownfacts7849

    3 жыл бұрын

    @@L2.Lagrange yeah, people need to grow up. Ik that he must be liking his maths professor who sleeps in the class and teaches nothing.

  • @imaybehot4734

    @imaybehot4734

    3 жыл бұрын

    wish my dad would do the same wish I have a dad

  • @ThisIsInnocent_YT
    @ThisIsInnocent_YT4 ай бұрын

    To Sum Up: For equations y=a sin(bx) and y=a cos(bx), |a| is the highest y value point on the graph and -|a| is the lowest y value point on the graph. |b| represents the frequency of the graph or 2pi/b

  • @jaor6449
    @jaor6449 Жыл бұрын

    bro is so good... thanks for saving my grades again!

  • @user-yg8kd6wg5w
    @user-yg8kd6wg5wАй бұрын

    Thank you,You have helped me a lot.

  • @jerrysanchez9098
    @jerrysanchez90987 ай бұрын

    You are the true Math Hero

  • @crisponyoutube
    @crisponyoutube7 ай бұрын

    best video I have found on this topic... last minute panic before my IB exam :D

  • @beigomaacademymathsclub5873
    @beigomaacademymathsclub58733 жыл бұрын

    Thanks for the video!

  • @lubilunbna1359
    @lubilunbna135911 ай бұрын

    It really helped thanks bro❤

  • @MwinzajeDanao
    @MwinzajeDanao4 ай бұрын

    Man, thanks. God bless you

  • @Poopsy_daisy
    @Poopsy_daisy2 жыл бұрын

    Thank you so much! You helped heaps, for some reason I don’t understand anything my teacher is saying ;(

  • @surajjani4868
    @surajjani48683 жыл бұрын

    Sir, your teaching style is so awesome

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    @edim.productions Жыл бұрын

    YOU ARE MY LIFE SAVER

  • @heist4420
    @heist44204 ай бұрын

    thank you so much, this helped a lot :)

  • @sarahjin5005
    @sarahjin50052 жыл бұрын

    Very helpful thanks sir

  • @alwayslearningC
    @alwayslearningC3 жыл бұрын

    Keep on moving sir 🙋🙋🙋

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    @CramMark3 жыл бұрын

    It’s an honor being the first person to watch one of your videos.

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    @user-od1ch7ru8o Жыл бұрын

    lets gooooo!!! crazy with math!!!

  • @mr.dinonugget1833
    @mr.dinonugget1833 Жыл бұрын

    this helped so much

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    @electricalnoobject50113 жыл бұрын

    Love you sir❣️

  • @AdeosunElizabeth
    @AdeosunElizabeth6 ай бұрын

    Thank you so much bro 😊

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    @siyabulelampinge5642 жыл бұрын

    You the best Sir we love you

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    @user-vy1dy6ih8e2 жыл бұрын

    I'm very lucky because I found your channel.

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    @sandeltra2 жыл бұрын

    thank you so much! God bless

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    @Erri2Sick Жыл бұрын

    dude you saved my life

  • @saysHotdogs
    @saysHotdogs Жыл бұрын

    This is the smartest man who ever lived and who ever will like literally people think I'm some kinda STEM queen but it's all this king

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    @legendaryboi99703 жыл бұрын

    amazing!

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    @calebquentel88372 жыл бұрын

    Saved my life

  • @alexgrant-explainingmaths8077
    @alexgrant-explainingmaths80774 ай бұрын

    Who taught this guy?! This guy knows everything in maths, chemistry and physics!!!

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    @alexanderhamilton58182 жыл бұрын

    You are carrying me through my pre calc course like Joe Burrow taking the Bengals to the Super Bowl.

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    @randommeep2 жыл бұрын

    thank you so much!

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    @user-dt7hc6ek4m3 ай бұрын

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  • @goodgalriri_
    @goodgalriri_6 ай бұрын

    Hi,just wanna enquire act y do we put pie values and not actual real values such as 90,180,360 and so on🤔

  • @jayx3843
    @jayx38432 жыл бұрын

    thank u my king

  • @auditor9927
    @auditor9927 Жыл бұрын

    The best video

  • @itamarb-e4088
    @itamarb-e40884 ай бұрын

    Why is it so easy for me to understand you and so hard for me to understand my teachers?

  • @demonslayereditsz
    @demonslayereditsz2 жыл бұрын

    Thank you

  • @marveladel7343
    @marveladel73432 жыл бұрын

    Thanks alot I am Egyptian but I like your explain it is so simple ♥️♥️♥️♥️

  • @tiffaroro4238

    @tiffaroro4238

    2 жыл бұрын

    Hello incase you need help in online classes,assignments and tasks ,I'm here to help you out.

  • @rithevikaravind815
    @rithevikaravind8153 жыл бұрын

    I've been waiting for this video

  • @varirejendiaende3315
    @varirejendiaende33158 ай бұрын

    Thanks Mr, but that function of y=2cos(x)-1 the period is in 360 degrees, or am I confused.

  • @pklarbipianoandrelaxation
    @pklarbipianoandrelaxation11 ай бұрын

    Thanks alot

  • @alexjeffin1186
    @alexjeffin11866 ай бұрын

    How did you get 3pie/2? 19:07

  • @jinnjinn5567
    @jinnjinn5567 Жыл бұрын

    you can also think of B as the number of cycles within a length of 2π

  • @yanoski9
    @yanoski92 ай бұрын

    I don't get it at the level of 15:15 because of the graph extending to 4pii and why is the negative y-axis is upto -3 .

  • @kamvc72
    @kamvc722 жыл бұрын

    Mistake at 21:48 it should be 5 pi/2 not 4. Great Video regardless.

  • @siddharthagautam8261
    @siddharthagautam82617 ай бұрын

    Amazing

  • @md.mahbubanamtanim9081
    @md.mahbubanamtanim90814 ай бұрын

    Thanks

  • @kingpeterdaroy9812
    @kingpeterdaroy98123 жыл бұрын

    Nice Explanation

  • @GabrielTobing
    @GabrielTobing5 ай бұрын

    Dude needs to be protected as a international treasure.

  • @SV42165
    @SV421652 жыл бұрын

    Now let's talk about.. graphing.. ..TRIGONOMETRIC FUNCTIONS.

  • @mattbenjaminpepito2823
    @mattbenjaminpepito28232 жыл бұрын

    may you have a good life

  • @alexjaehyunfan
    @alexjaehyunfan2 жыл бұрын

    I wish you were my maths teacher.

  • @AngellaBakali-jf6tg
    @AngellaBakali-jf6tg11 ай бұрын

    Wooow thanks

  • @happyvirus6590
    @happyvirus65903 жыл бұрын

    Do you have a video for Analysis of Variance (ANOVA)?

  • @isaiahfigueroa6422
    @isaiahfigueroa6422 Жыл бұрын

    Thanks big dawg🫡

  • @sambi8074
    @sambi8074 Жыл бұрын

    At 21:50 the number in between 5 and 1 should be 3 on the y-axis of the graph.

  • @BethlehemFetene-gs9ms

    @BethlehemFetene-gs9ms

    11 ай бұрын

    There is 2 at the middle. Its just cause the amplitude is 2 he shifted the graph 2 units up and down from 3 which will bring us to the numbers 5 and 1 respectively.

  • @rayanmalla4139
    @rayanmalla4139 Жыл бұрын

    I'm absolutley speechless .

  • @nightmarefredbear7739
    @nightmarefredbear77393 жыл бұрын

    I wonder why there is a person disliking this..

  • @Bangtan_Vibes_7

    @Bangtan_Vibes_7

    24 күн бұрын

    I think, the people who disliked this video are our professors who always fail to teach us smth properly💀

  • @omyjonhgod
    @omyjonhgod Жыл бұрын

    EOC next week wish me luck guys

  • @syedmdabid7191
    @syedmdabid71912 ай бұрын

    What's the period of the function y= sin x + cosx???

  • @thatomofolo452
    @thatomofolo45211 ай бұрын

    Let's go 🚀🥳🤸🦅💪💫

  • @biblefae
    @biblefae Жыл бұрын

    yooo i love u ❤

  • @isagani9048
    @isagani9048 Жыл бұрын

    at 17:45 isn’t the general form of sine function is asinx(bx-c)+d?

  • @zayn-xw6ru

    @zayn-xw6ru

    Жыл бұрын

    No it is + c

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    @asnappinturlaa3 жыл бұрын

    i love youuuuuuuu

  • @sanopann1896
    @sanopann18967 ай бұрын

    how do you know how many key points the graph are that's where I'm having a hard time

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    @maryjohnson15683 жыл бұрын

    Stock can drop from top to bottom and still be a 60 bagger. All this in 10y. investing is a very long journey where our temperament gets tested. have to have the capacity to suffer for long periods. have lived through the examples above, naming the stock today is pointless.

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    @georgesmith9461

    3 жыл бұрын

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    3 жыл бұрын

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    3 жыл бұрын

    Yeah what type of Investment y'all are into the stock market has been crashing lately.

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    3 жыл бұрын

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    3 жыл бұрын

    Investing in cryptocurrency and gold which is better?

  • @glasssmirror2314
    @glasssmirror23144 ай бұрын

    I don't know whether the same media teachers who teaches excellent way will do the same in schools institutions.

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    @jonastyloggers3358 Жыл бұрын

    i love you

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    @mamoako1521 Жыл бұрын

    13:09 TS

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    @MadiatlaFortunate2 ай бұрын

    Guys how can one get his email address I want to join the membership