I often do lookup these trig identities from the back of my trig identities book, but I seldom try to demonstrate them. I suppose that if I was teaching, I would draw from some the more obscure ones and choose them for demonstration to my class, blackpenredpen sure does a good job at this.
Hey, here is a puzzle about finding cos(nx) recursively if you wanted to try it: Let fn(x) be a polynomial such that fn(cos(x)) = cos(nx), so for example f1(x) = x, as cos(x) = cos(x). Show that f(n+2)(x) = 2x f(n+1)(x) - fn(x), and hence find cos(4x) in terms of cos(x)
What about using this theorem to provide a formula for say: cos(nθ) and sin(nθ)? Is it possible and if so I'd be intrigued to see you do a video on it! 😊
@liewsernjet2163 hahaha when I wrote this comment I was in my first year of undergrad maths degree, I have since gotten my degree and forgotten how to do most of this lol
Speaking of DeMoivres formula: I didn't know you could prove this inductively, so you don't need to start with Eulers formula. In fact that's the easiest way to get Eulers formula.
Oh! Franchement j'ai aimé beaucoup cette vidéo merciii , le théorème de Moiver est assez facile maintenant Et que tu fasse quelques vidéos de matrices et les applications linéaire Vous êtes vraiment super-prof je vous remircie du fond de mon cœur !
De moivres theorem never heard but isn't that just eulers formula with some basic exponent rules? Sure i would have taken two steps instead of one to get to (cos theta +isin theta) ^3 going over e^3 theta=(e^theta)^3 and then putting the identity back in, and then I'd probably mess up mulipying things out to be perfectly honest xD
Your method is correct, but originally, before Euler came up with that formula, De Moivre discovered his rule and proved it for all n. Of course, now with Euler’s formula, the proof is much easier
You can't assume that the power rule holds for complex exponents, but De Moivre proved it to hold in such special cases when the second exponent is an integer.
Сергей Мишин ur statement I am not from a pure science background so probably I didn't understand what you said. I just solve math equations and learn from videos so maybe there r certain things that I may not be knowing. That's why I want you to explain
Hey I have a question for you, solve and find the answers for 10^x=x+100. I know there should be 2 answers because of the graphs of the functions. But didn't know how to really solve this equation. I read about the W-Lambert function which helps solves this, I didn't fully understand how to use it. Can you explain that please?
That app didn't get the French pronunciation right. I would bet Dr. Payam would say "duh MWAH-vruh." That said, words do enter English with different pronunciations. So it might be "duh MOY-vuhr" in English.
14th comment here Hi blackpenredpen! I am struggling so much trying to find how to find the sin or cosine of theta. no, not theta as in like 150 degrees or 60 degrees (a multiple of 5), i wanna know how to do something like 167 degrees, 78 degrees, 13 degrees, something that isn't a multiple of 5. I really need help with it (well, not having an exam next week, i just had my death exam in math (which was easy for me). I'm 10 so i don't have ideas for it). May you make a video about it please. :) don't worry i know radians, i just think degrees is easier to understand... (don't even try the addition, subtraction, or square adding formulas(is there even a square adding formula?), it doesn't work.) proof: squaring the numbers ending in 1, 2, 3, 4, 6, 7, 8, 9 will not be a multiple of 5. so, trying to get a square root that results in a number ending with 5 or 0 will be impossible if you square root a non-multiple of 5. addition and subtraction will result in a multiple of 5 if you use multiples of 5 in addition or subtraction. please help me :) I believe you can do it. :)
The answer is that for 99% of use cases, we don’t bother trying to find an exact answer. People long ago found close decimal approximations for all the integer degree values of the trig functions and compiled them into trig tables. Today we just use a calculator. So sin(167) = 0.22495...
I don't want to use a calculator. Are all high school students that lazy in finding values of trig functions? i mean what i could do is for example: 25 / 25 = 1 but then is there any division solution for it or multiplication? sin( 25 / 25 ) = ?(25) ? ?(25)... so yep, and here is when multiplication is needed. sin( 25 / 25 * degrees ) and that's a complete problem for us.
Robert doesn't really help, but i could divide the chord into half and the angle too. then divide the chord into 120 pieces and that's the sine, right?
Cubic equations: /watch?v=yY09LFn06nc Quartic equations: /watch?v=32JL_ZAIDo-I As for quintic equations, it is not possible to solve a general quintic equation, as proven by Abel in 1824. EDIT: Typo
I often do lookup these trig identities from the back of my trig identities book, but I seldom try to demonstrate them.
I suppose that if I was teaching, I would draw from some the more obscure ones and choose them for demonstration to my class,
blackpenredpen sure does a good job at this.
Ok guys in this video I will have my voice back, isn't it
Ok guys in this video I will have my whiteboard and markers back, isn't it
Moon man?
Yes. Try more of this. Make exact sin() and cos() for all the angle at 1° step from 0° to 90° by using this formula.
Thanks a lot, it helped me. I was confused about where the 4 comes from. Good explination..
Great video! Months ago I liked maths but never had an interest for trigonometry, you have changed that, thanks!
Hey, here is a puzzle about finding cos(nx) recursively if you wanted to try it:
Let fn(x) be a polynomial such that fn(cos(x)) = cos(nx), so for example f1(x) = x, as cos(x) = cos(x).
Show that f(n+2)(x) = 2x f(n+1)(x) - fn(x), and hence find cos(4x) in terms of cos(x)
What about using this theorem to provide a formula for say: cos(nθ) and sin(nθ)? Is it possible and if so I'd be intrigued to see you do a video on it! 😊
De Moivre's Theorem : For all integers n, it satisfies: cos(nθ)+ίsin(nθ)=(cosθ+ίsinθ)^n
@liewsernjet2163 hahaha when I wrote this comment I was in my first year of undergrad maths degree, I have since gotten my degree and forgotten how to do most of this lol
Shout out to my boi De'Memes.
finally got it afta watching so many similiar videos, ur the best!
you have done what my lecturer failed to do. thanks.
Speaking of DeMoivres formula: I didn't know you could prove this inductively, so you don't need to start with Eulers formula. In fact that's the easiest way to get Eulers formula.
this was very helpful, thank you
So helpful! You are a really good teacher
Você é incrível 🔥 🙏. Não entendo nada do que você fala mas entendo tudo o que você escreve. Obrigado 😁
Your videos are amazing! They actually made me interested in math!
ty so much, very usefull from Spain
If sin(3x) = -4sin^3x + 3sinx , cos(3x) = 4cos^3x - 3cosx,
what is the simply value of tan(3x)??? Please help me to find it... thanks...
AMAZING EXPLICATION 😁😁
Damn, I can understand your approach much more easier than my professor
Great video. Thank you so much
Whoa! That just blew my mind.
Manas Tiwari But my mind was blown when I found out that the USSR still legally exists.
Сергей Мишин When was that?
Manas Tiwari 3 months ago. But the Russian Federation is actually fake. It's not a state at all.
Can you do a proof for fractional powers when using De Moivre's theorem?
Where do you recommend I could practice my integrals? I already have a brilliant.org subscription but Wolfram Alpha looks good too
THANK YOU 🙏🏼
This man is out here saving my math HL ass once again
So sick!!
Oh! Franchement j'ai aimé beaucoup cette vidéo merciii , le théorème de Moiver est assez facile maintenant
Et que tu fasse quelques vidéos de matrices et les applications linéaire
Vous êtes vraiment super-prof je vous remircie du fond de mon cœur !
De moivres theorem never heard but isn't that just eulers formula with some basic exponent rules? Sure i would have taken two steps instead of one to get to (cos theta +isin theta) ^3 going over e^3 theta=(e^theta)^3 and then putting the identity back in, and then I'd probably mess up mulipying things out to be perfectly honest xD
Your method is correct, but originally, before Euler came up with that formula, De Moivre discovered his rule and proved it for all n. Of course, now with Euler’s formula, the proof is much easier
You can't assume that the power rule holds for complex exponents, but De Moivre proved it to hold in such special cases when the second exponent is an integer.
Wonderful video!
You’re a life saver
Amazing Videos! Keep it up!!!
Oon Han hehehe, you too!!!!
Math is so beautiful
Rash Scientist Mathematics with the i (imaginary unit) is not mathematics at all.
Сергей Мишин ?
Rash Scientist What didn't you understand?
Сергей Мишин ur statement
I am not from a pure science background so probably I didn't understand what you said.
I just solve math equations and learn from videos so maybe there r certain things that I may not be knowing.
That's why I want you to explain
Rash Scientist Do u know what the imaginary unit is?
Thank you
Wow You Made It easy 💓
Hey I have a question for you, solve and find the answers for 10^x=x+100. I know there should be 2 answers because of the graphs of the functions. But didn't know how to really solve this equation. I read about the W-Lambert function which helps solves this, I didn't fully understand how to use it. Can you explain that please?
Yuval Tuby hey you can use Taylor series expansion for 10^x to get a polynomial eqn and solve it for x
You could solve it graphically.
That's a great idea!
Sir please could you upload a video like this with higher powers and coefficients like 51 or 251 instead of 3?
Nice video
Next time you should call Peyam to pronounce the french and german names for you^^
AndDiracisHisProphet that's a great idea!!! How come I didn't think of this earlier
That voice wasn't Dr Peyam??? XD
close, but not exact :D
Very nice, thanks a lot :)
Thanks
Hey please solve the integral of
1/(x+e^x) & (cos(x^2))/(x^2)
That app didn't get the French pronunciation right. I would bet Dr. Payam would say "duh MWAH-vruh."
That said, words do enter English with different pronunciations. So it might be "duh MOY-vuhr" in English.
Great English ❤
Thanks a lot
TH-cam recommend this video after doing this question in final
THANK YOU!!!!!
14th comment here
Hi blackpenredpen!
I am struggling so much trying to find how to find the sin or cosine of theta.
no, not theta as in like 150 degrees or 60 degrees (a multiple of 5), i wanna know how to do something like 167 degrees, 78 degrees, 13 degrees, something that isn't a multiple of 5.
I really need help with it (well, not having an exam next week, i just had my death exam in math (which was easy for me). I'm 10 so i don't have ideas for it). May you make a video about it please. :)
don't worry i know radians, i just think degrees is easier to understand...
(don't even try the addition, subtraction, or square adding formulas(is there even a square adding formula?), it doesn't work.)
proof:
squaring the numbers ending in 1, 2, 3, 4, 6, 7, 8, 9 will not be a multiple of 5. so, trying to get a square root that results in a number ending with 5 or 0 will be impossible if you square root a non-multiple of 5.
addition and subtraction will result in a multiple of 5 if you use multiples of 5 in addition or subtraction.
please help me :) I believe you can do it. :)
The answer is that for 99% of use cases, we don’t bother trying to find an exact answer. People long ago found close decimal approximations for all the integer degree values of the trig functions and compiled them into trig tables. Today we just use a calculator. So sin(167) = 0.22495...
I suggest you read about "half-angle formulas" and also "Ptolemy's table of chords".
I don't want to use a calculator. Are all high school students that lazy in finding values of trig functions?
i mean what i could do is for example:
25 / 25 = 1
but then is there any division solution for it or multiplication?
sin( 25 / 25 ) = ?(25) ? ?(25)...
so yep, and here is when multiplication is needed.
sin( 25 / 25 * degrees )
and that's a complete problem for us.
Robert doesn't really help, but i could divide the chord into half and the angle too. then divide the chord into 120 pieces and that's the sine, right?
btw robert there is a part there where you have to do this same process all over again.
Very useful
Please make video solving cubic and x^5 equations
Cubic equations: /watch?v=yY09LFn06nc
Quartic equations: /watch?v=32JL_ZAIDo-I
As for quintic equations, it is not possible to solve a general quintic equation, as proven by Abel in 1824.
EDIT: Typo
No birds were injured in making of this video. :-)
Thanx! ☺
Whoa, this is easier than expanding from 3x=x+2x 😮
Why is the Doraemon song playing in the background?
แบลกเพ็นเร็ดเพ็นดีมากเลย
this is just the euler’s formula
you're the best
سیگنال؟
*W H E R E A R E Y O U R F I N G E R S ?*
YAY!!!!!
I love you. ❤
more
Doraemon in bg for intro
I bet you could prove that you could kill two birds with one stone
Thank you sir😂😂😂. I'm first viewer.😂😂😂🤣🤣🤣
Watashi wa hontōni kono chan'neru ga daisuki. Tried my best to translate😂
TyronRaza 3915 Kono chaneru wo hontōni watashi wa daisuki
Insert meme: "Well, I'm kind of a scholar myself"
Doraemon
first
Thanks
Thanks