Graphing Sine and Cosine Trig Functions With Transformations, Phase Shifts, Period - Domain & Range

[@TheOrganicChemistryTutor]

Trigonometry - Free Formula Sheet: bit.ly/47diggI Trigonometry Video Lessons: www.video-tutor.net/trig.html

[@algtkz]

I owe u my diploma man

[@emmamorrison5065]

you just took an entire unit of conusion and summed it up in 18 minutes....thank god. Happy finals everyone

[@mariorl8927]

Emma Morrison Bro its my second week at high school and I have an AP test :(

[@saint8350]

God*

[@emmamorrison5065]

@@saint8350 you’re a silly goose

[@saint8350]

@@emmamorrison5065 God* not "god".

[@emmamorrison5065]

@@saint8350 oh my god you’re so silly

[@jackdavis8596]

Small error @4:33, should be 2, not 3 pi, but otherwise great job.

[@bananaman-cv3rn]

thanks i was really confised

[@spiral09]

@No Sirens u gay

[@Dominiccoll]

OH MY GOR THANK YOU I WAS SO CONFUSED

[@MeiziVu]

thank god..... was so lost... so it's 6pi wide then, yeah?

[@sake7855]

@@MeiziVu ya It should be 6 pi and I was also looking for the comment pointing it out so I didn't get the wrong information

[@faizanhussain9377]

The amount of times I've found myself coming back to this amazing guy, is beyond me. He has helped me for so many years. Forever grateful for you lmao.

[@imadiboyy]

Fr

[@jeffreyhaydinjr7400]

I’ve been watching him since freshman year of HS I’m now a sophomore in college

[@ARTales32]

You are the best because I had tried multiple videos on youtube, but no one explains it like the way you did. EASY AND SIMPLE. Thank you, trillions of times.

[@LightWaIker]

Only trillions? :)

[@b0ld651]

woah lil uzi learnin math

[@whitneyc4238]

AGREED

[@anudeepannangi9813]

WHAAAT? Still searching KZbin for math help Are the videos from 2006 really helping? Me: YES, they are!

[@rayankhan3858]

Exactly, i just got the same ad

[@brylhd1939]

Mine too

[@alio6051]

The videos from 2006 don’t help..at all!!!

[@yalkn2073]

Math didn't change much since 2006. Math is math

[@SG-we9gq]

Yalkın ÇIRAK they mean the topics, atleast here in Britain the maths curriculum has massively changed, was really easy and simple back in the mid 00’s and is now pretty difficult, it fluctuates really, I knew someone who did their a levels (equivalent to Americans doing their finals or sats or whatever) in 99 and 00 and they said it was really difficult whereas I know people who did a levels in 08 and they said it was pretty easy the only difficult thing is that the internet was not used much in revision, mostly old school text book work so they didn’t have the resources myself and my current year group have which is apparently why a levels have gone back to being difficult.

[@tmn671]

These are the kind of videos that don't die. 6 years later still very useful Thank you

[@sanopann1896]

big bro i need your help at 10:24 how did he get the 5pi

[@tsheringyuden18]

yes rightly said

[@credible3203]

@@sanopann1896 pi/2 + 2pi Now, this can also be written as pi/2 + 2pi/1, because 2pi divided by 1 is = to 2pi. Now, when adding fractions, you need to make the bottom number, (denominators), the same. So we currently have pi/2 + 2pi/1 So we times the 2pi/1 by 2 all together to make the denominator the same as pi/2 That leaves us with pi/2 + 4pi/2 Meaning we can add the fractions together, when adding fractions we don't add bottom number, as it will change the value. So pi/2 + 4pi/2 = 5pi/2 Hope this helped.

[@catalinamendez7489]

I was extremely concentrated and un minute 11:50 it scared the crap out of me. LOL Anyways, thanks for the video!!!

[@PSIRCULplayforfun]

it actually scared me 😂😂

[@princeatsrim3159]

😂😂😂😂

[@khanyisilemahlangu5139]

😂

[@Jeremy6638]

same lol

[@samuelrestrepo4489]

Learned more in 18 minutes than in 4 hours of class. thank you!

[@IceOfPhoenix88]

200th like ;)

[@cho2447]

still learned more in 18 minutes than whole week of classes. Thank you!

[@orsall2084]

my teacher does not teach, but this video teaches me :)

[@nikitasharma8664]

Summary: for *y = a sin (bx + c)+ d* or *y = a cos (bx + c) + d* |a| = amplitude 2π/|b| = period -c/b = phase shift d = vertical phase shift Domain: ℝ Range: [-1, 1]

[@sikey8154]

And you are a hero

[@d3ixi]

⚡️

[@thatomofolo452]

🎉

[@parkerturner1018]

you are amazing

[@hyperkinetic_]

chad

[@velveteencherrytart6335]

i love how all of us in the comments are struggling together. wow what a team :)

[@leendowdlamz]

I know hey🤣😂

[@teikay9076]

We're in this together bro

[@markvincentgamos383]

Lol waaaaaawaaaaa

[@tyrapp2202]

Big fax

[@Boy-cm8ec]

Yes. I also struggling. Need this for Fourier series... God help me.

[@amaya.a6596]

I know you posted this exactly a year ago but i just want to say you helped me understand this whole unit on these trig functions graph. I really appreciate it. Thank you so much

[@TheOrganicChemistryTutor]

No problem

[@PSIRCULplayforfun]

2 years to be precise now it 2019

[@billhaxley8873]

Its 2021-er now

[@noface8705]

@@billhaxley8873 damn time flies doesnt it

[@narrek6600]

@@noface8705 I guess so

[@-sma-8743]

can we please just appreciate how this man saved our life .... thank you !!!!!

[@shengxyoojblue]

My teacher is no help with this at all, but this really helped me understand it better.

[@troybrown0102]

Having the same issues as we speak

[@andersonbrizuela2112]

@ That proves that everyone makes mistakes, so you always gotta check twice, or three times

[@swirlpuffy]

Same here! I'm understanding this much better than how my teacher taught it in class.

[@BoloSFXkviewshoursago]

@Always study time or maybe he just can’t teach well lol

[@eternalyap]

Mechanic: So what sound is your car making? Me: 11:50

[@user-fo4ue9mo4z]

I don’t see it

[@ExoHazzy]

@@user-fo4ue9mo4z You're supposed to hear it

[@eternalyap]

@MaVi DeNiZ you must be fun at parties.

[@graceyoung2743]

LMAOOOOO

[@nethmalperera3681]

omg this is funny, you made my day lol

[@steverogers1630]

All of my online college chemistry and math classes have used this guys videos to teach their classes. I have never met nor seen most of my professors and at this point I honestly feel like this is my real professor. So just want to drop a quick thank you from me and all of my fellow class mates who have received degrees because of your online lessons. I feel like HCC owes you some money!

[@javaDB.1.0.V1]

What kind of incompetents would simply link these videos and not teach? Then what are you paying for... the degr-oh wait.

[@FOkoro100]

Wrong calculation with the period of 3cosx/3... you wrote 9pi as the period instead of 6pi... please make that correction..thanks

[@xoydas1783]

Yes

[@frostbitepokin9520]

Fuck

[@vidsforfun5155]

FrostBite Pokin LMAO

[@Jassosilly]

Omg yes i just saw it and went looking for the comments !!! I thought i was trippin

[@MrLred125]

shut up Fred u douche

[@EG-no9ns]

Night before the unit test gang☝🏼😎

[@syedrehan4294]

Yesssssir

[@zebibasolomone1272]

Me after 3yrs😢

[@daddyfwine6122]

morning of test 🔥🔥

[@NtlakuBaloyi]

Let's go!

[@melmarie6083]

Yurrrr

[@isabellasadler8323]

omg, this video was so helpful! I literally understand everything now. Thanks for being more of a teacher than my actually teacher! :)

[@mayerlylara1600]

MoOd

[@imhulki463]

Omnipotent headass

[@victoriazuniga-lopez956]

I learned more from your 18 min video than from an entire weeks worth of school lectures. Thank you!!! You are a life saver👍🏼👍🏼👍🏼

[@kennethpkfr]

This guy sounds like a teenager but he's smart as hell

[@iknowyouseeme3233]

Isn't this stuff pre calc?

[@kennethpkfr]

@@iknowyouseeme3233 but check out all of the other stuff he teaches on his channel

[@Andrew-md4oi]

I know you see me this is pre-calc? Fuck my algebra 2 teacher

[@iknowyouseeme3233]

@@Andrew-md4oi pre calc summarizes all of algebra 2 so there is significant overlap

[@iknowyouseeme3233]

@Quinzel Sabina what does this have to do with what I said?

[@TahirAhmad-io6uw]

You actually make things simple and straightforward. Thanks so much, I literally took a day trying to understand this stuff.

[@sankhiero]

At 4:33 the period = (2pi)/(1/3)=6pi . Thanks for the great video!

[@Emmaaa_02]

Thanks to you, my physics grade went up from a B- to an A! And now I'm hoping to get my B- in Pre-Calc up tomorrow. I have a test on this material and these videos are really helping me review. Life saver.

[@jahnj2523]

Is physics harder or easier than pre Calc?

[@Bryan-eq6nt]

@@jahnj2523 can't compare cus physics is logic, theory and calculations whilst pre calculus is just straight up solving. Luckily pre calculus usually just involves you putting values into functions. Honest opinion: pre calc is much easier than physics

[@AvrieDavis]

I have my IB math exams this Thursday and Friday and this video helped to teach me in 20 minutes what was failed to be taught over 2 years. Thank you so much!

[@hiradbasiri2248]

how was tour exam?

[@isaacliu._.6899]

I have watched your videos to pass honors chem, ap chem, and now math. You are truly a blessing to this world. From the bottom of my heart, my most sincere thanks.

[@AK47ASSASSIN2]

Bro i would give you a kiss right now if i saw you. Failed my maths exam cause of this last year, kept coming across vids that were leaving out one important part here and there. You summed it all up perfectly and so easily. Massive respect, great teacher.

[@saint8350]

Jesus is Lord

[@Code_mood]

I don't know what I would do without you. First physics and now math, you're the best teacher.

[@zanders.7816]

You explained this better than my college professor. Thank you so much for everything your channel does!

[@sanopann1896]

big bro i need your help at 10:24 how did he get the 5pi

[@zanders.7816]

@@sanopann1896 To add fractions, you need a common denominator so instead of 2pi/1 he multiplies the 2pi by 2 to get 4pi/2 which he added to the pi/2 to get 5pi/2.

[@Nic-of1sr]

Thank you soooo much. My trig prof is terrible and thinks you won't really learn how to do it unless you start off with the hard problems. I was so lost. You really helped me understand the concepts in your step by step approach. I really appreciate you taking the time to make this video!

[@drunkenarsonist7253]

Thank you my friend; you've been helping me for the last 2 years and I always appreciate the work you put in!

[@bell893]

There is a mistake at 4:33 where you accidentally switched the 2 for a 3 in the period formula.

[@priyetam-george5662]

noticed that too

[@parteeksaini2725]

yes I got confused so I I started looking at the comments for the answer thx for clarifying

[@akbarbaig5134]

yea i got mad confused

[@Ophelia1111]

bro! when was there!! i was like "what" and read the comments kkkkk

[@kareemmarshall6440]

I feel it was deliberate... to make us minions feel like we just corrected a pro. We are now officially smarter than him 🤓🤓🤓

[@Bonksy42]

Never have i ever liked math as much as when i watch your videos. Youve helped me so much through so many exams and i understand math much much more since i started watching yiur vids! Thank you for existing

[@Mooksie]

OMG this video is a life saver. Going through the same problems on a separate sheet of paper is really instilling the steps into my mind. Thank you!

[@risabee6312]

With the one mistake aside (which is already addressed in other comments), this is a pretty solid video. Thanks for the guidance and explanations! I appreciate all the different scenarios/examples.

[@khanhluu7006]

I love how clearly you demonstrate your lecture in this video, much better than my teacher, this is also why I always have to go on KZbin again for the same lecture

[@prsstnc]

same

[@timi8272]

Question: when calculating for the period at 4:33, you used 3TT(pie) instead of the normal 2TT, why is that?

[@Hollows1887]

It was a mistake. Periods for sin and cos are 2pi/B. Tangent is the exception being pi/B.

[@timi8272]

Oh okay, thank you for the clarification. Really enjoyed the video!

[@royerelvir5400]

I was so confused as well

[@Katy-Peace]

Yes, maybe he just forgot, and the period in that example is 6 pie

[@jayjbee6214]

I had to double check on google and typed in the problem lol it suppose to be 2pi/ 1/3 = 6pi

[@drstoned8523]

i wonder how it feels like to read so many comments of appreciation...definitely deserved ....been out of HS for many years and just started uni, your videos are inredibly helpful..

[@kateyash8779]

When youtubers that you can watch for free teach math a better way than profs in your colleges that you had to pay expensively for lmao🤣

[@chewyn6696]

University is for certification, not education.

[@ja1pa]

@@chewyn6696 Wish I woulda been told sooner, but my ass is struggling in calc

[@donaldrenfroe9984]

@@ja1pa same, but I'm in PreCal, I'm a junior in high school

[@paulsiameuni3439]

for real😅

[@huhohyeah3049]

11:50 helicopter goes off

[@renaruseva3800]

Who’s watching in the morning of your exam???

[@BelaBela-t7z]

Me

[@EpignosisGodsRhema]

😅

[@marialinsay3762]

Me

[@Buddy2356-]

Shii, im watching it 20 min before it

[@Jos_7382]

Me

[@maica2476]

You know, our teacher is a very yood instructor. I fully understand what he was sayin' when I was sitting in his class yet here I am watching your video becoz I have a short term memory I think. Your video's awsome. You're as good as my teacher. I just really hope that it will stay in my coconut shell until our semifinals.

[@PYROMANIAN777]

This was FAR more helpful than the textbook. Thank you!

[@КириллКлимушин]

This is by far the best thing i would recommend to watch to anyone who is starting out with signal processing.

[@luukipuuk3537]

Im trying to get into uni and need a math certificate for that. Videos in my own language rarely hit the spot. This explanation was awesome and really helps!

[@ethanlinger2123]

Did I really just learn all this in 18 minutes. You’re awesome man

[@yyzzur]

Thank you sir!! I'm studying STEM still in gr.11, I hope I will be an engineer someday🤗

[@KenMyles-xt2yw]

Thanks for your black background and very visible and clear writing and graphs. I've seen others on KZbin. No others are as clear and visible as yours. Also your explanations are not rushed but rather at a pace sufficient for teaching and learning. Thanks again. ( I often share your videos with other students. They too are grateful for your videos. ) May you continue to have success.

[@dk57nde23]

i swear nobody even comes close to being able to explain complicated math shit as smoothly as this guy does.

[@green_razor8569]

Bro I was legit struggling on khan for like more than 3 hours and I come on here and almost completely understand it in 8 minutes ...

[@linh1752]

SAME LMFAOOO I was doing problems and khan and got like half of them wrong

[@Astroacid]

only go to Khan if you have the time and want a deep understanding of the concept

[@manymanytacos8082]

Oh my god that makes so much sense, I have 50 minutes before my math final you are such a life saver

[@wendyrivera8789]

I just wanted to empathize how thankful I am for these videos and I wish I am as knowledgeable as you are one day. I haven't been at school in years and I been struggling a lot. You're videos have definitely helped. THANKS 🧡

[@TheBlackFriesian]

11:49 headphone users at max volume RIP. MHHHMMHMHMMHMHMHMMMHHM.

[@theflash691]

😂

[@rahul7976]

🤣

[@ariesfundales9644]

AHAHAHAHAHAHA

[@misscrazylearner7220]

Thnx in advance

[@joelcastillo5828]

Thanks

[@쩡지니]

you are my life saver. thank you so so so so so much 😭 I couldn’t have even attempt it if it wasn’t your video. My teacher is so bad I always have to teach myself a lesson 😭 your video helps so much. Thank you A LOTTTTT

[@Seopotify]

쩡지니 헐 한국인!!!!!

[@love_leeyu]

우앙 한국인이다!!

[@not_youraveragejoe]

I have an applied math exam tomorrow, and this guy is the reason I'm gonna pass :) thank you, you've saved my life, genuinely! I've learned more from this video than all of this semester

[@bbqchickenlemon]

You explained this better than any teacher or other video I had :3

[@glasssmirror2314]

Now I have reached my destination after several crash-landings in other lectures. I salute you sir and tks a billion.

[@Anon.thoughts]

Thank you as always! Your videos are amazing. I did notice though on you 3cos(1/3x) graph, you said the period was 9pi but it would actually be 6pi. Or am I missing something?

[@guest6114]

No youre right, 2/ 1/3 is 6

[@morby1296]

You r right. Cos has a period of 2 pie

[@TheLazyLarryShow]

I noticd that error too.

[@TheLazyLarryShow]

Having said that, it is a very helpful video!

[@Lightinthedark10323]

I noticed but had questions. Thank you for asking, and thank you, everyone, for your answers.

[@Sultan_A]

Very Good, The Organic Chemistry Tutor, Keep It Up!

[@hope-tn1oz]

Man, thank you very much for all the help youve given to us. If not for you I wouldnt have 90+ grades every quarter all these years since my math is hard carrying me. I appreciate it very much.

[@MatthiasRegisRict]

I’ve spent over a week in class trying to understand this and you taught me in less than 20 minutes. I can’t even

[@o0DjMiX0o]

Whenever I'm lost in class I turn to his videos, you're the real MVP

[@gailb6406]

u have a talent to express clarity im not kidding. I have more of a pictures mind and u totally put this in my head better than a teacher could ever

[@MegaTheman25]

Great vid man. Gonna save my ass for this math test in trig tmmr lol.

[@kyliemiller173]

it’s been 2 years how was the test

[@wael-mentalhealth]

@@kyliemiller173 he fucked it thats why he didnt respond back leave him alone wtf is rong with you now he is depressed because of you and society will fall down because of your comment are you happy???

[@somxr_738]

@@wael-mentalhealth lmao

[@phucphannguyenhong0314]

I'm from Vietnam My Professors teach me in Vietnamese but i cannot understand But you teach in English and i can understand all . Thank you so much !

[@advita7816]

Hey great video! At 4:51, didn't you mean to write 2pi instead of 3pi? I tried graphing the function and the period showed as 6pi, whereas you've written calculated 9pi. Great video though! Thanks :)

[@bonsaigamer3320]

I was wondering the same. Got me real confused

[@prodbyree]

This man has saved my life so many times dude

[@simtsan2504]

With this whole online schooling thing, I'm failing math for the first time, there's no pulling my marks out of the gutter now, but when I take the course again next year hopefully I'll get it. This 18 minute video is more helpful than my teacher's hour long lesson.

[@ramiroalonso9985]

you've honestly helped me more than any college professor or hs teacher , thanks man

[@adamharoon6021]

8:01 This happened cause the horizontal distance between a midline intersection point and a consecutive maximum point is 1/4 of a period. With this same logic... the horizontal distance between a maximum point and a consecutive minimum point is 1/2 of a period. Hope this helped!

[@mariah.___xp]

bro i got so discouraged going into my trig class because i felt so stupid, not knowing what to do or understanding the lecture in class. however, i feel a lot better now after you dissected it for us. thanks :)

[@GusGames10]

I took trigonometry in college. My professor was an engineering and he programmed for NASA, and his hobby was to teach math, a mean he is a beast but I didn’t learn how to graph sin and cosine with him until now 🌝 He was just writing in the whiteboard assuming we all now that. Btw I asked to many classmates and they didn’t understand too.

[@davidchepkwony6155]

U 've made many learners know something.God bless u sir

[@bread9072]

Broo y'all can't lie that sound at 11:50 caught me off guard 😭

[@janetadeo4046]

This must be the great video so far.. in the videos I have been theyre only discussing the properties and not teaching how to solve.. a life saver indeed

[@a.graciesmith7766]

i did in fact have a breakdown before coming here, somebody needs to fire my pre calc teacher

[@loveofaflower5486]

When you clear your throat it scared me- but thank you sm for the lesson I love ur videossss!!!

[@sguniska]

You sir have no idea but you are doing God's work

[@azi9_ity]

(he knows)

[@sanopann1896]

big sis i need your help at 10:24 how did he get the 5pi

[@sguniska]

@@sanopann1896 well 2pi is the same as 2pi/1 and to add fractions you need the same denominator which is 2. So you do (2pi/2)×2 and that is 4pi/2. Then 4pi/2 +pi/2 is 5pi/2

[@duckman12569]

You've helped me a lot with my online diploman man, just wanted to say thanks. You condense a lot more in a short span than these unit coordinators manage to convey.. wish my course was as valuable as the cost.

[@IKdeoSSa_7]

6:08 That moment 😂. Great video man; really appreciate it.

[@idahd6705]

You have made my life so much easier I kept on getting this topic wrong thannnnkk you :)

[@kay2337]

period is 2pi/b not 3pi/b at 4:34

[@usernohandle]

thought i was bugging

[@Cholienne-hy9sn]

thanks, I thought I was wrong

[@issy0812]

i was about to say

[@ShurooqFadhil-lx8fp]

Trig is a tough topic, but you make it easier and more understandable, thanks from the bottom of my heart🙂

[@janetnyanor3739]

Thank you so much, you just saved my grade.

[@kanaotsuyuri546]

Thank you so much, you couldn't have explained this better, my math tutor explained this to me and I didn't understand a word she was yapping out of her mouth. Now I understand! I might just pass my exam lmao.

[@ariannaelise6930]

honest to god if my professor taught me this I would never have been CONFUSED

[@raizenzoldyck7563]

then you realized you’re professor is the descendant of Confucius LOL

[@juliandavis7457]

studying for the accuplacer in an attempt to skip Algebra 1 classes in dual enrollment. You sir, are awesome

[@HapPy-mf8dg]

WOW THANK YOU SOOOOOOOOOOOOOOOOOOOO SOOOOOOOOOOOOOOOOOO MUCH

[@nikitasharma8664]

what the hell.

[@merma9042]

thanks man. This helped me learn everything I slept through this week.

[@Bea-gc5ti]

i have a trig test tomorrow; i’m debating playing this on repeat as i sleep so i can memorize it in my mind 😅😅😅

[@prsstnc]

that's not how the brain works :)

[@biancacubelo738]

Thanks for the very helpful video. In the span of 2 min, I was able to learn more than what my math teacher has taught me in a week. Giving this video a thumbs up fs 100% very helpful video!

[@dizviz6939]

I agree with this comment very much. This comment read my mind and took the words out of my mouth. Thumbs up. I approve. Love it 6000000%!!!!

[@revolution6424]

11:49 When your car won't start.

[@aumpatel6571]

Bro, nice!

[@khanyisilemahlangu5139]

😂

[@whoknows23838]

7 years later and this is still helping people like me, thank you!

[@dandyremix2360]

You are a freaking legend.

[@DDMouse-fj7gf]

you are a literal life saver even now when im in coñlege

[@XietMakpie]

11:49 This scares me, not gonna lie, given the fact that I'm wearing earphones.

[@271skippy]

This was the single most useful video I have found on how to graph sinusoids. Thank you for posting!

[@ruramuchenga4623]

He explained so beautifully 😭❤️❤️I vow my teacher could never

[@thenomad9963]

Sameee.. my teacher in HS literally just drew stuff on the board and basically made us do it on our own. I'm a senior about to enter college in the fall, and I'm just trying to refine most of the math I was supposed to be taught in junior year+, bc i wanna be an engineer. thank god for the internet.

[@DarrellBarnes]

Thank you! Attempting to to the Khan Academy Trig modules and I got stuck on the horizontal phase shift. 9:42 Thanks for reminding me to set the inside equal to zero (and solve for x) to find the phase shift.

[@jingasura9381]

Thank you for making this easy to understand video