You and Organic Chemistry Tutor were the only persons who let me understand this topic. Thank you so much for making online classes a lot easier. :'>

@rahultr7198

3 жыл бұрын

Me too

@mushtaqrasool9169

2 жыл бұрын

this is why we have such teachers that actually care about people understanding the concept instead of the student grasping it on his own. Thank you, professor, for getting into our lives

@suzywhall9494

Жыл бұрын

So accurate!

@pausasil7867

7 ай бұрын

😅

@Gd_Monsterforce

2 ай бұрын

Fr

learned more from this 12 min video than 2 weeks in class

Thank you for this video, sir! My vision for beginning a math video series has "everything" you did here: limited review, error-free content focused to match the title, and scripted conversation. I love the graphing technology and the exit ticket. I watched dozens of videos and got very discouraged before arriving at this one. Awesome job!

@ProfessorDaveExplains

5 жыл бұрын

be sure to check out my whole mathematics playlist!

@ivoryas1696

2 жыл бұрын

​@@ProfessorDaveExplains Once I stop being not-so-good at math, I, for one, plan to. Under the assumption that it'll help my physics understanding, of course not exclusively 😅

A complete year without a good explanation about this particular topic. You are doing it great guys, thanks so much

hey man you are doing great keep making such videos. i dont why you get less views. but keep doing this you are really inspiring me and my friends to learn.

Ap chemistry, math placement tests, this guy has always got my back and makes things simple and quick

you’re heaven sent whether it’s for math or chemistry. thank you so much for uploading these

Great explanation, I appreciate how you connected this to the unit circle. It does clarify things.

It makes sense he teaches Italian, math, physics, chemistry... It's Jesus! Hahah :P

@EugenMarianPopescu

5 жыл бұрын

Jesus didn't know how to write, so... :P

@enzoqueijao

3 жыл бұрын

_Praise italian Jesus!_

@mustafazafar2137

3 жыл бұрын

Jesus spoke Italian?

@viennasausagelover96_29

Жыл бұрын

He does Italian?? Holy shit smart

@papapicolo2594

9 ай бұрын

and has long hair🤣

It's like a rollercoaster! I'm glad he mentioned comprehension.

professor dave, organic chemistry, and fort bend tutoring are my three avengers in learning math

The perfect video I was looking for to help my kids with Intro to graphing Trig functions, THANKS

His first video on this playlist solved one of my biggest confusion ....thank you sir......And I love your intro song sir🙂

Prof dave i learned a lot thanks for the video please keep making such videos so beginners can understand things thanks a lot prof

Hi! Not getting why we divide by two when finding the phase shift of "y=4sin(2x -2pi/3)"

My best teacher ever your explanation is so wonderful loving your lecture

Getting me on track, prof dave

Excellent job for giving valuable information...

this channel saves my life all the time

Such a summary about Trigonometric Functions is really hlepful

Excellent video!

You are underrated!!! You should get over 10 million subs!!! Best of luck

Very helpful sir keep uploading

Thanku sir your graph each and every value which is important

but we can also plug in complex arguments in trig functions and get all numbers on the complex plane. Are there any ways to visualize complex angles like in sin(2+3i)=9.15-4.169i, how can we visualize angle (2+3i)? or is it just rigorous mathematics?

@ProfessorDaveExplains

6 жыл бұрын

oh man, i dunno! i know there is a way to plot complex numbers on the coordinate plane, but i'm not sure how to plot them as angles. something to think about!

Wowwwwww kep up the good work professor dave

Thankyou so much

Are pi or 2pi the same in the comprehension case?

Professor please i do not understand? This seems very strange of a subject to me. Where can I further observe this?

y = sin (2)x is a horizontal compression it would be a horizontal stretch if you had a fraction instead of (2).

Thanks!

Please make videos on more difficult trigonometric identities

why did u do 2pi-3/2 i don't get that part at all

I feel like at 6:25 horizontal shift should have a - in front of it, just like we've seen in the videos before

I would like to watch your precalculus playlist after completing trigonometry playlist

thankyou sm 😭

thanks a lot.

so blessed to learn maths from jesus himself

I think we can say you might be better than Eddie Woo!!! very nice video indeed; thanks allot! ❤❤

I see it now lol thank you for your vivid explanation!

Weird. I don't have a 480p or 720p resolution options available? Idk what's happening

@Jam-zt4xe

4 жыл бұрын

You came from future

Hi Dave, I do not understand the last part of the transformation... y=4sin(2x -2pi/3), when we do the phase shift, -2pi/3, why do we have to divide by 2? thanks

@user-tb7jq8vv1u

3 жыл бұрын

y=4sin(2x -2pi/3) -> 2x - 2pi/3 = 0 -> 2x=2pi/3 -> x=pi/3

@MedK001

2 жыл бұрын

You have to divide by 2 because the period was changed (x got multiplied by 2)

Why did you divide by two when finding the phase shift? Is it because the horizontal stretch of 2 (the coefficient of x) is causing things to compress? If so, what is the relation between the two? Also, I am referring to 7:58 in the video.

@mushtaqrasool9169

2 жыл бұрын

i am not dave but pretty sure he did that for the reason you mentioned, because I tried and my computer died

@heliomiranda9622

9 ай бұрын

I think the purpose is just to adjust the "proportion" of the phase shift to match with the compression caused by the two to the "x"... then the relation between the two is just to make things inversely proportional or else the graph would have a big shift instead of the half of it related to the compression... so if it was 3(x) the phase shift would be (2pi/3)/3.

dope vid davey boy

Could you maybe explain how to do the tasks at the end?

@user-xt9bm6ix7w

3 жыл бұрын

It's been a year you've probably figured it out, but for those having the same question in the future. Prof explained in the video that the period = 2π/b where b is the horizontal stretch. The first question is saying period is 4π then 4π=2π/b then you can figure what the horizontal stretch is

1:32 there's an error - instead of y=cos(theta) it should be x=cos(theta). If this wasn't confusing enough, further on in the video, x is used to represent an angle theta...

@ProfessorDaveExplains

3 жыл бұрын

Functions are traditionally represented with a y. That is examining the domain and range of y = cos(theta). And the angle can be represented with any variable, we normally use x and y when representing functions, so that works just fine.

Thx for your videos professor Dave! I can't get how x/2 and 2x appeared in the task :( Are you just dividing 2π/4π to gen 1x/2 is case with sin and 2π/π to get 2x in case with cos?

@ProfessorDaveExplains

6 жыл бұрын

yes that's right!

Sir..... While we graph the trig functions.....is the domain in radians and is it becoz we cant have domain in degrees? For example sin x graph... All x values are in radians?

@ProfessorDaveExplains

4 жыл бұрын

You can do degrees it’s just that radians is more standard

@carultch

2 жыл бұрын

Mathematicians prefer radians on these functions, because it makes the Calculus a lot more simple and elegant. You can have the domain in units of degrees, it just means that there is a conversion factor inside the function, and that conversion factor accumulates through the chain rule when you use Calculus on these functions. For instance, the derivative of sine is cosine, when the input units are radians, which keeps it simple. But when the input units are degrees, the derivative of sin(x) is (pi/180)*cos(x). There is also nothing special about degrees, as we've arbitrarily defined the full circle to be 360 degrees. It has its advantage because it can be divided in to an integer by all numbers from 1 thru 10, with the exception of 7. But radians have the advantage when it comes to further mathematics, such as Calculus, which is why mathematicians prefer radians.

5:44 how is the period of the function pi, but also 2pi/b which one is it?

@Belmont1714

4 ай бұрын

The general formula of a sine wave is : y= A sin (Bx+c) + D. Since B is 2 and one full revolution is 2pi you divide the two's. 2pi/2 = just gives pi. So since it is pi, you'll have to make the wave to just the period of pi. One full cycle is pi here.

@MXGIRL87

3 ай бұрын

@@Belmont1714 thank you!

Love from india

Prof in 8:01 i didnt understand why u divided 2 pi/3 by 2 wouldnt that change the magnitude of the horizontal shift

@heliomiranda9622

9 ай бұрын

I think the purpose is just to adjust the "proportion" of the phase shift to match with the compression caused by the two to the "x"... then the relation between the two is just to make things inversely proportional or else the graph would have a big/disproportional shift instead of the half of it related to the compression... so just on the "graph representation" if it was 3(x) the phase shift would be (2pi/3)/3... if it was 4(x) the phase shift would be (2pi/3)/4... and so on. :)

hey I don't know if you are still replying to comments but I have been trying to get ahead of my class in school and do trigonometry in my free time however I cant seem to understand how you got to tan=sin/cos could you please help me thank you

@ProfessorDaveExplains

4 жыл бұрын

just start at the beginning of the trigonometry playlist!

@karmansingh6926

4 жыл бұрын

Professor Dave Explains thank you very much I had just figured it out and I just want to say I love your stuff and please keep these educational videos coming :)

7:36 why over (as opposed to times) that term?

@carultch

2 жыл бұрын

The term multiplied by the input is called the angular frequency (traditionally noted as omega). It has units of radians per second, or degrees per second, depending on the choice of unit for your trig function. Period (traditionally noted T) has the unit of seconds per cycle. To get from angular frequency in radians per second to period in seconds, you use dimensional analysis, to cancel the radians, convert to cycles, and to get seconds in the numerator. (omega radians/second) / (2*pi radians / cycle) = frequency f in units of cycles per second or Hertz. Take the 1/frequency to get the period in seconds per cycle.

🙏 Thankyou sir From India your student 😅Neva

Hello Dave. I dont really know if u still answer questions, but I need help to the first question of the comprehension. I am little confused, since cos(2x) is a period of pi.. How can sin(x/2) give a period of 4 pi? Mvh. Mathias.

@rocks7456

3 жыл бұрын

I'm not Dave, but maybe I could help make it clearer for you, so here :>> We can use the formula for the period of the cosine function 2π ÷ |b|. In the function y = sin(x/2), we can say that x/2 can be expressed as (1/2)x, or one-half times x. From there, we have b = 1/2 (since it is the number by which x is multiplied). Plugging it into the formula for our period, we have 2π ÷ |(1/2)|. Another way to look at it is 2π ÷ |0.5|. Hence, the period will be equal to 4. :>

@user-uh3ew1rj6u

5 ай бұрын

Hey! You are confusing with period which is 4 pie and general x, they are inter-related but general way of saying sine(4x) not sin(4pie), so to get x first convert this 4 pie into x. which will be x/2 with the formula that he has mentioned. Hope this can also help you, as I was having this issue but try to sort my own and want other also to understand quickly ). Ciao

Why do you have divide the phase shift by 2?

@brightminds7194

3 жыл бұрын

For x = pi/3, y =0

Awesome!! Thank you so much. Clear concise, and includes everything needed. You're Jesus (and look like him toooo)

Thanks for sharing! I posted a video on explaining the sine graph. Let me know your thoughts.

I'm confused about something in this video. You can see in the 1:05 that the range of trigonometric function are the possible sine values but then when it goes in the 1:16 it says that the range of trigonometric function is -1≤y≤1. How did it change from being all possible sine values to -1≤y≤1? I'm literally confused here?🤔 Can someone explain?

@Wutheheooooo

4 ай бұрын

it is just all possible sin value, bigger than -1 and smaller than 1

@Wutheheooooo

4 ай бұрын

sin value can be everything in between but not bigger than 1 or smaller than -1

Done.

What about in degrees?

@carultch

2 жыл бұрын

Mathematicians prefer radians on these functions, because it makes the Calculus a lot more simple and elegant. You can have the domain in units of degrees, it just means that there is a conversion factor inside the function, and that conversion factor accumulates through the chain rule when you use Calculus on these functions. For instance, the derivative of sine is cosine, when the input units are radians, which keeps it simple. But when the input units are degrees, the derivative of sin(x) is (pi/180)*cos(x). There is also nothing special about degrees, as we've arbitrarily defined the full circle to be 360 degrees. It has its advantage because it can be divided in to an integer by all numbers from 1 thru 10, with the exception of 7. But radians have the advantage when it comes to further mathematics, such as Calculus, which is why mathematicians prefer radians.

Hi, didn't get why we have to divide phase shift by 2 😅 Thanks.

@mercurius1488

Жыл бұрын

Me too

thank you math jesus

I have a question, um why does a trigonometric phase shift have to be divided by b and other functions don’t? ..... or do they?

@carultch

2 жыл бұрын

Given the parent form of a trig function: y = sin(x) Now add an amplitude A, and angular frequency (B) to it: y = A*sin(B*x) Now suppose we want to shift it to the right, by a time shift of C. Locate x, and enclose it in parenthesis. Subtract C from x inside those parenthesis. We subtract from x to shift right, we add to x to shift it left. y = A*sin(B*(X - C)) If you distribute B among the terms in the parentheses, you get: y = A*sin(B*x - B*C) The term B*C becomes the phase shift, that is traditionally noted as phi. It has units of radians, assuming the sine is configured for radians as the input unit. We could also shift this vertically, a distance D, that is called the offset. y = A*sin(B*x - B*C) + D This is the general equation for a sine wave, that is shifted C units to the right, and D units vertically. It has an amplitude of A, and an angular frequency of B. Its period would be 2*pi/B, assuming the x units are radians.

@rodger3352

8 ай бұрын

omg, thank you so much for the effort ! :)) @@carultch

But cos is x Isn't

WHAT THE HECK IS COS AND SIN

Blessed be your name, Trigonometry Jesus, may you forgive our computational errors, and gives us our daily formulas, for now as it is in our Pre-Calculus Class, Amen

PEAK OF ADHD!

Not understanding anything ? It's maths . I have failed in maths in my 12 th stdio. lol .

@ProfessorDaveExplains

6 жыл бұрын

if this is confusing start from the beginning of the trigonometry portion of the series!

@sushilthakre5492

6 жыл бұрын

Professor Dave Explains OK Sir I will do that. I want to improve my maths.

This makes no sense

@ivoryas1696

2 жыл бұрын

Gradeoff What part about it?