Visual Calculus: Derivative of sin(θ) is cos(θ)

Build an understanding behind different concepts of calculus that will help you tackle challenging problems at:
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Proof: Derivative of sin(θ) is cos(θ)
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Programs used:

- Cinema 4D
- Processing
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Music by Zeeky:

"Saw you"

[JM-usfr]

Dude, you’ll never run out of geometric proofs to do. These are awesome videos, keep up the great work.

[eamon_concannon]

At 1:14 you did not explain why the angles labelled alpha are equal. The reason is that the upper alpha is the angle between the horizontal and the tangent. Since the radius is perpendicular to the tangent, we have
alpha + theta = 90. The small triangle at top right is an approximation to the small dark region. The angle inside of it (indicated by alpha) is an approximation to alpha which approaches alpha as delta_theta approaches zero.
This is a very nice proof and I love the channel.

[Wildlon]

The last part was a bit clunky. You didn't need to use similar triangles. Top left angle on the triangle is theta. Then it's obvious that cosθ = ∆y/∆θ just from using the smaller triangle.

[Invalid]

Excellent video/proof!
👏 👏 ☺

Edit:
You deserve so much more subscribers, the quality of your videos is amazing!

I shared this everywhere I can. ☺

[josephcooper]

This video made me want to cry, it’s so eligantly beautiful. It makes me see why so many have pursued mathematics with the passion that they have. It truly is the pathway to hope and reason.

[Magnasium]

Beautifully done. Proof shown visually without any talking and minimal written explanation

[stevemallot]

Dude! Where were you when I was in high school? Oh, wait. Where was the internet?

[michaelrosenberg]

SO THAT'S WHY


WHY DIDN'T I THINK OF THAT?


THAT EXPLAINS SO MUCH!


GEOMETRY'S SO PRETTY THANK YOU!

[fwcolb]

Yes, this is intuitive because the sine wave and cosine waves are 90 degrees out 0f phase.

[yaaryany]

Seen this before in one of the 3b1b's essence of calculus episode. And it's absolutely fantastically Awesome! You deserve way more subscribers!

[Zokalex]

I honestly didn't understand very well. I actually understand it more the mathematical way. I understand until 1:38, I don't know what the similarities are and what they play

[JohnBicknell]

I can prove it analytical, but this is far more satisfying.

[vpambspt]

Wow, powerful!

Nice song as always, fits really well!

[atomiccompiler]

Thank you for uploading this today, I was having a hard day and this made a smile on my face. <3

[brucelickey]

I'd love to see a follow-up of this demonstrating why the derivative of cos(x) is -sin(x).

[mangalbaskey]

Presentation style is so good.
Nice work.

[ToniBrasil]

I never understood that way before....thanks a lot, from Brazil 🙏

[OneWeirdDude]

That was awesome, you didn't even need trig identities. Good work.

[XuanNguyen-opqs]

Damn, the beat drops so sick, I can't even focus on the visualisation 😂

[BigDBrian]

note that the circle segment 'triangle' approaching a right triangle is essentially the limit as x goes to 0 of sin x / x being 1.