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
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 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 😅
For who didn't get it: take " y=Asin(Bx-C)+D " A: is the amplitude The distace between the horizontal axis and the max/min of the function. B: affects the period and the phase shift To find the period, we take " period=2π/B ". C: affects the phase shift The phase shift is "C/B", that's why I wrote that B affects it. D:affects vertical shift If positive, it goes up by D. If negative, it goes down by |D|. Hope it helps.
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.
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...
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.
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.
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.
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?
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!
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?
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.
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. :)
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?
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
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
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 :)
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
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
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?
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.
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.
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.
![ทุกครั้งที่หลับตา (Lucid Dream) - AYLA's [ Official MV ]](http://i.ytimg.com/vi/4i1OBAQyv58/mqdefault.jpg)
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. :'>
Me too
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
So accurate!
😅
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!
be sure to check out my whole mathematics playlist!
@@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 😅
For who didn't get it:
take " y=Asin(Bx-C)+D "
A: is the amplitude
The distace between the horizontal axis and the max/min of the function.
B: affects the period and the phase shift
To find the period, we take " period=2π/B ".
C: affects the phase shift
The phase shift is "C/B", that's why I wrote that B affects it.
D:affects vertical shift
If positive, it goes up by D. If negative, it goes down by |D|.
Hope it helps.
It makes sense he teaches Italian, math, physics, chemistry... It's Jesus! Hahah :P
Jesus didn't know how to write, so... :P
_Praise italian Jesus!_
Jesus spoke Italian?
He does Italian?? Holy shit smart
and has long hair🤣
you’re heaven sent whether it’s for math or chemistry. thank you so much for uploading these
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.
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...
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.
thank you my man, was thinking the same. It just is very confusing that y is both a cardinal and a random incognita, but good prof dave replied.
this channel saves my life all the time
Such a summary about Trigonometric Functions is really hlepful
professor dave, organic chemistry, and fort bend tutoring are my three avengers in learning math
so blessed to learn maths from jesus himself
You are underrated!!! You should get over 10 million subs!!! Best of luck
Ap chemistry, math placement tests, this guy has always got my back and makes things simple and quick
A complete year without a good explanation about this particular topic. You are doing it great guys, thanks so much
Thanks!
Getting me on track, prof dave
🙏
Thankyou sir
From India your student 😅Neva
Thanku sir your graph each and every value which is important
Love from india
Please make videos on more difficult trigonometric identities
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.
i am not dave but pretty sure he did that for the reason you mentioned, because I tried and my computer died
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.
y = sin (2)x is a horizontal compression
it would be a horizontal stretch if you had a fraction instead of (2).
Very helpful sir keep uploading
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?
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!
It's like a rollercoaster! I'm glad he mentioned comprehension.
I feel like at 6:25 horizontal shift should have a - in front of it, just like we've seen in the videos before
5:44 how is the period of the function pi, but also 2pi/b which one is it?
@@Belmont1714 thank you!
in that problem pi was a result of dividing 2pi by 2, and remember b=2 here, so 2pi/b = 2pi/2 which gave us "pi" for this problems period
Professor please i do not understand? This seems very strange of a subject to me. Where can I further observe this?
Awesome!!
Thank you so much. Clear concise, and includes everything needed.
You're Jesus (and look like him toooo)
I would like to watch your precalculus playlist after completing trigonometry playlist
Hi! Not getting why we divide by two when finding the phase shift of "y=4sin(2x -2pi/3)"
inverse solutions across = axis when solve for x or y, inversely x / are ±
I think we can say you might be better than Eddie Woo!!! very nice video indeed; thanks allot! ❤❤
My best teacher ever
your explanation is so wonderful
loving your lecture
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?
You can do degrees it’s just that radians is more standard
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.
Prof dave i learned a lot thanks for the video please keep making such videos so beginners can understand things thanks a lot prof
Excellent video!
Prof in 8:01 i didnt understand why u divided 2 pi/3 by 2 wouldnt that change the magnitude of the horizontal shift
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. :)
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?
it is just all possible sin value, bigger than -1 and smaller than 1
sin value can be everything in between but not bigger than 1 or smaller than -1
His first video on this playlist solved one of my biggest confusion ....thank you sir......And I love your intro song sir🙂
why did u do 2pi-3/2 i don't get that part at all
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
y=4sin(2x -2pi/3) -> 2x - 2pi/3 = 0 -> 2x=2pi/3 -> x=pi/3
You have to divide by 2 because the period was changed (x got multiplied by 2)
Thankyou so much
Wowwwwww kep up the good work professor dave
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
just start at the beginning of the trigonometry playlist!
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 :)
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
Could you maybe explain how to do the tasks at the end?
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
Are pi or 2pi the same in the comprehension case?
Weird. I don't have a 480p or 720p resolution options available? Idk what's happening
You came from future
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?
yes that's right!
Done.
thanks a lot.
The perfect video I was looking for to help my kids with Intro to graphing Trig functions, THANKS
Hi, didn't get why we have to divide phase shift by 2 😅
Thanks.
Me too
thankyou sm 😭
Excellent job for giving valuable information...
dope vid davey boy
thank you math jesus
I see it now lol thank you for your vivid explanation!
Why do you have divide the phase shift by 2?
For x = pi/3, y =0
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?
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.
omg, thank you so much for the effort ! :)) @@carultch
But cos is x
Isn't
What about in degrees?
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.
7:36 why over (as opposed to times) that term?
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.
Thanks for sharing! I posted a video on explaining the sine graph. Let me know your thoughts.
Not understanding anything ? It's maths . I have failed in maths in my 12 th stdio. lol .
if this is confusing start from the beginning of the trigonometry portion of the series!
Professor Dave Explains OK Sir I will do that. I want to improve my maths.
im cooked on text
WHAT THE HECK IS COS AND SIN
Check earlier Trigonometric videos first.
PEAK OF ADHD!
This makes no sense
Gradeoff
What part about it?