My heart fills with so much joy after watching your video. This one too was a perfect cocktail of Geometry, Calculus and algebra. Love you bro. God bless you.
I dont understand why you have so many less subscribers like your videos are so interesting and I just stare at the screen, becuz you made learning so interesting and easy. Thank you. I understood it so well
So funny. I watched yesterday your video about derivative of sin and the referred video was not available anymore about the cos identity and here is a new one.
Thanks for the video. My question for the second part is, if we have two number number multiplied to be 1, but one of it is zero in the end, then how it can be one when multiplied to another number?
You should not assume one of them is zero. Remember, the limit is about 'as x approaches a point'. It doesn't mean x gets to that point. Good thinking, though.
The sin theta part was taught beautifully but I didn't get the cos theta part because we had to prove = cos theta -1/theta=0 but here you got 1-COS THETA/theta = 0?
I noticed something in the second proof: lim[(1-cosθ)/θ][(1+cosθ)/θ]=[lim(1-cosθ)/θ][lim(1+cosθ)/θ] It's the identity lim ab=(lim a)(lim b) We must have both lim a and lim b exist. But lim a is not known yet.
Even though you don’t know it exists at the time. You can prove it exists after using the epsilon-delta definition I believe. That being said, I’m just a high school student who isn’t the most mathematically inclined. So I might be wrong
Question: When we divide the equation by sinΘ, how do we determine that sinΘ > 0? Because when sinΘ ≤ 0, the equation will change. Can someone explain what happened in this step?
Because theta is equal along all terms. If it was negative in all of the then we would multiplying the entire inequality by - 1 and get back to the case where theta was posetive in the first place.
Sir do you have courses you teach,Iam considering on taking refresher courses,for one Iam a senior citizen,but my interest in learning will never die,and I would like to incorporate your incredible talents into my life so I my expand upon my own profession for GODS HONOR,I hope and pray this to become a reality.Thank You For Your Time Of Day Sir-GOD BLESS
I can always remember how to prove sinx / x, but (1 - cosx) / x always throws me. I don't think I've seen it solved this way before, or maybe I have but I just can't remember. Either way, I like it!
11:34 here it doesn't make sense if you want to use the squeeze theorem. In fact it doesn't make sense at all since this is what the squeeze theorem implies. Let me show you what I mean. If 1 0 sin x/x
My heart fills with so much joy after watching your video. This one too was a perfect cocktail of Geometry, Calculus and algebra. Love you bro. God bless you.
I dont understand why you have so many less subscribers like your videos are so interesting and I just stare at the screen, becuz you made learning so interesting and easy. Thank you. I understood it so well
Prime Newtons always proves he is always worth watching! 😊🎉
thank you for making my life simpler
Wow never had this explained to me in such great detail. I always was told because of the squeeze theorem…but to see it like it makes TOTAL SENSE!
I love your CVD clips.
Extraordinary lecture. This man's name shall be told.
凄いわかりやすくて助かりました！
so great, I completely understand. thanks sir
Thanks for this amazing video 😊
I would use double angle identity
and Pythagorean identity
cos(theta)=cos^2(theta/2) - sin^2(theta/2)
1 = cos^2(theta/2) + sin^2(theta/2)
Yep!
Thank you sir ❤
Superrbb teaching 👍🏻
So funny. I watched yesterday your video about derivative of sin and the referred video was not available anymore about the cos identity and here is a new one.
Love it
Thanks
Try not to use L’Hôpital💀💀💀
Thanks for the video.
My question for the second part is, if we have two number number multiplied to be 1, but one of it is zero in the end, then how it can be one when multiplied to another number?
You should not assume one of them is zero. Remember, the limit is about 'as x approaches a point'. It doesn't mean x gets to that point. Good thinking, though.
awesome, how did you squeez "Limits" to the description title?
The sin theta part was taught beautifully but I didn't get the cos theta part because we had to prove = cos theta -1/theta=0 but here you got 1-COS THETA/theta = 0?
Their both the same thing the negative sign just goes to zero
@@vivekranavaya4043 oh ok thanks 😁
I noticed something in the second proof:
lim[(1-cosθ)/θ][(1+cosθ)/θ]=[lim(1-cosθ)/θ][lim(1+cosθ)/θ]
It's the identity
lim ab=(lim a)(lim b)
We must have both lim a and lim b exist. But lim a is not known yet.
Even though you don’t know it exists at the time. You can prove it exists after using the epsilon-delta definition I believe. That being said, I’m just a high school student who isn’t the most mathematically inclined. So I might be wrong
Thanks for an other video....mas than Iran
Question: When we divide the equation by sinΘ, how do we determine that sinΘ > 0? Because when sinΘ ≤ 0, the equation will change. Can someone explain what happened in this step?
can i please know why you put the equal sign for the inequality?
1. a>b => a≥b
2. a≥b => a>b
1 is legitimate but 2 is NOT.
So feel free to use 1 whenever it's helpful.
well done! 👏🏼
Thank you!! 😁
Why area of sector is not (pi*r^2*theta)/360????
Can you do more proofs?!!!!
9:46 why assume theta is positive what if it for negative?
If we consider theta as negative may be it between -1 to +1 at 11:55
Because theta is equal along all terms. If it was negative in all of the then we would multiplying the entire inequality by - 1 and get back to the case where theta was posetive in the first place.
Tremendous approach.
Greeting From Curaçao An Island Nation in The Caribbean
Greetings!
thank you very much and much ! keep it up!
Sir can i write this annual exam??
Love your video super great on your explanations looking forward to more of your videos,thank you for your great work
Sir do you have courses you teach,Iam considering on taking refresher courses,for one Iam a senior citizen,but my interest in learning will never die,and I would like to incorporate your incredible talents into my life so I my expand upon my own profession for GODS HONOR,I hope and pray this to become a reality.Thank You For Your Time Of Day Sir-GOD BLESS
Excellent
when the equal sign is validated in the inequaity please
1. a>b => a≥b
2. a≥b => a>b
1 is legitimate but 2 is NOT.
So feel free to use 1 whenever it's helpful.
I can always remember how to prove sinx / x, but (1 - cosx) / x always throws me. I don't think I've seen it solved this way before, or maybe I have but I just can't remember. Either way, I like it!
11:34 here it doesn't make sense if you want to use the squeeze theorem. In fact it doesn't make sense at all since this is what the squeeze theorem implies. Let me show you what I mean. If 1 0 sin x/x
Awesome!!!!!!
Thanks!!
watermelon :) If I said it in the classroom I would be kicked out :)
Watch out professor, because the area of the sector explained would be: (theta/2π) (π.r²) = theta/2.
We are dividing by Zero in the second proof. That cant be right.
Many and tragic Mathematical errors !!! Ask Mathematician .
The integrity of a true mathematician. 🎉
I hope I'm consistent. Thank you 😊
What a teaching skill ❤
anyone from 11th tamilnadu
Me..
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