Graphing Transformations with Sine and Cosine (Precalculus - Trigonometry 12)

[@rahulkiroriwal8779]

he will never stop teaching

[@Heavenlight100]

Hopefully

[@BeWaReJay]

This aged terribly :(

[@austinoquinn815]

I have some bad news

[@collina.7336]

I know you get a lot of praise, but I don't think it is adequate. You sir are a national treasure. Thank you so much for your contribution to society.

[@averageyoutuber-kk5ly]

im not kidding. my trig teacher should be fired and they could just save money by paying you and showing your lectures. you teach better than pearsons online courses and my teacher and textbook combined. thank you so much. please never stop teaching. you were born for this

[@shayanali8771]

Best thing happened to Calculus since Newton and Leibniz themselves. Our Professor Leanord!

[@stephaniewallace5785]

this is so helpful. im taking online trig with no lectures and this is life saving or at least grade saving

[@takuyamatsuda7214]

I love you Prof Leonard. I'm taking math seriously late in the game because I never thought it'd benefit me for what I wanted to do. Now that I'm going into tech and I need Calc 1+2+3, diff eq, etc, etc, I seriously love you Prof.

[@frankieramos8017]

Me too what tech field are you going in?

[@Ahmedshorts12]

im going into machine learning what about you@@frankieramos8017

[@MakSte]

If there's a definition of a professor then professor Leonard fits it perfectly. He explains complicated concepts in a very simple manner.

[@adoniskon1783]

god bless this man! THANK YOU FOR YOUR CONTRIBUTION

[@frankieramos8017]

what job are you getting

[@fuadsadudin1972]

I wish I knew you when I were In highschool😢😢so grateful to know you now🙏🙏

[@georgesadler7830]

Professor Leonard, thank you for another Incredible video/lecture on Graphing Transformations with Sine and Cosine in Precalculus. Over time, I found Graphing Transformations with Sine/Cosine highly problematic, however, from watching this video and doing some problems increase my knowledge of the subject. These are different ways to do these types of problems which can be confusing.

[@anwaralenazi8879]

I hope you continue teaching forever.. for infinity ❤

[@SB-uv2xs]

Professor , YOU.ARE.AMAZING! btw did you stop teaching at college? because i love when you interacted with students , you seemed happier than now , talking to the camera.

[@julianscott4682]

His students always have cough. : )

[@mickeyp6639]

No he didn't. He even mentions in a recent video that he hasn't taught anyone trig that he also has calc which to me implies that he doesn't teach trig, but perhaps I misinterpreted that. But back to the point, basically he doesn't have to *put it on* like he would knowing he's not only teaching a class but also doing a video. I'm happy to know he's able to be more relaxed. It's gotta be obvious, let him alone about it about it and get to calc if you wanna see Leonard on the Stage again haha

[@satioOeinas]

amazing work Dr. Leonard

[@jeffcrain9757]

Very good job Professor Leonard! Trig is some scary stuff in calculus. If you don't have a good feel for it. I've really enjoyed your pre-cal youtubes. I've never seen it taught this way. But it makes a lot of sense.

[@حنان-غ9ذ]

باع المشاهدات يربي شكد قليلة 😔 تروحلك فدوةةة المليون والمليونينن عيناي💋

[@raghadalabead7603]

Thank you so much ❤️ I will watch all your lessons you are the best keep it up 👍

[@Blueskybuffalo]

Professor Leonard is smart, communicative and attractive. Why doesn’t he have a Netflix show? He can reboot Mathnet. Solving crimes using math!

[@jenniferwayment3770]

Happy PI Day Professor.

[@TzZek]

Tangent coming soon, can't wait for inverse trig functions.

[@kaelart5876]

do you happen to watch the whole series?

[@ebruakyar2816]

Hi professor, do you have any recommendation youtube channel for physics ? I am begging you , by the way , you are awesome!!! I passed my calculus2 final thanks to you

[@chitraajanth6369]

Wonderful explanation

[@wesselpretorius4345]

Thanx professor leonard

[@cacogato882]

How many more lessons of this series will there be? Btw thank you so much for your lessons!! They are great!

[@vijayfn6936]

Thank you so much!!

[@farhanhasankhan3113]

G.O.A.T

[@pizzamayani2166]

Is this the end of the series or there is still some contents to show?

[@kaelart5876]

Hi professor, I'd like to know how many more episodes is this series gonna have, I'd like to finish the whole course over my 2 month summer vacation. I want to know how I would schedule my days

[@مفكال]

Some time omega is placed in front of x and other times they use t, this confuses me.

[@مفكال]

Are these standing or progressive waves?

[@mahmodmoghaddam.p9277]

very good

[@sebqz6903]

my answer for the last exercise is: y= -3 cos ( pi/4 . x )

[@rozha3963]

amazing !!!!!!

[@beulahwilliams8885]

I can understand the way it is suppose to be but I do not understand the material base

[@madelinegonzales8229]

I have watched about 100 of your videos and I am so thankful for what you do. However, this video has me so frustrated because I do not understand the key points what so ever. Can you please make a video showing where these numbers are coming from in these examples? I don't understand where you are getting your numbers from. The example at 48:35 (0,1) (pie/4, -1) (pie/2, 1) I cannot for the life of me understand where that's coming from. On my unit circle, 0 = (1,0) not (0,1), pie/4 is (root 2/2, root 2/2) not -1, and pie/2 is (0,1) not (pie/2, 1). I know this professor has been MIA for a year, so if anyone see's this comment and understands please help.

[@DWILLMVP1]

I would STRONGLY recommend you rewatch video #84 (the previous video) because he will explain it better than me, but here's a quick explanation. You have to remember that for the function f(x)=cosx, x does not represent the x-coordinate on the unit circle, it represents a central angle on the unit circle, and then our cosine of that central angle gives us an output (the x-value on the unit circle here). Cosine only make sense when associated with central angles. We take an angle from our unit circle and plug it into our function, your traditional "x", and it spits out our "y" value which is the value on the unit circle. For example, f(0)=cos0 is actually asking, what is the value (output) of cosine on the unit circle when we have a central angle of 0? Well, it's 1, giving us the point (0 (input, central angle, 0 radians), 1 (cos, output value, our "x", adjacent over hypotenuse). I know it's hard to wrap your head around this idea, but just remember that x's are just blank spaces, and that here we're plugging in central angles on the unit circle for our x's, and getting our values based on the sin/cos/tan, etc. of that angle (coordinates on the unit circle). Again, you have to rewatch video#84, he specifically answers your question from minute 1-4.

[@musikparadise8911]

You mean pi/3 times 1/2? 23:58

[@musikparadise8911]

I get it

[@livingonmars6056]

Can anyone tell me why it is 2pai/3 on 22:29?

[@aizen_2k]

A little late but it's because 2pi/3 is 120 degrees.

[@فاطمةعلي-ذ8ك]

I need help l need partial differential equations

[@mohammedzaid537]

Sir i want to contact u if possible since u are really inspiring

[@musikparadise8911]

I thought cosine would never be reflected b/c it's an even function.

[@sulkyghost1107]

He is Look Like Matt Demons 😂

[@jaibahuguna3818]

How the number before x affects the period . Can anyone please explain?

[@avigitdasgupta7549]

It stretches or compresses the period, if the omega increases the overall period for sin greater than 2pi it means, the period has been stretched by the omega and vice-versa.

[@jaibahuguna3818]

@@avigitdasgupta7549 now I get it. Thanks.

[@Newzisiun]

💕

[@Kevin-cc3up]

💯

[@johnbiluke8406]

Hm, profound.

[@Butterfly-fd6pr]

😩😩😩 I HATE math!!!