Picture me Differentiating (visual calculus)

Correction: at 03:54, I should say “perpendicular to the radius of the circle at the point” for clarity.

In this video, we investigate the derivative of the sine function experimentally and analytically. The analytic (limit-definition) proof relies on two limits that are often computed geometrically, so this poses the question: is there a visual proof that the derivative of the sine function is cosine? We then show a wonderful visual proof that demonstrates that this derivative fact is true by using a similar triangle argument.

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This animation is based on a visual proof by Selvaratnam Sridharma from the September 1999 issue of The College Mathematics Journal (https://www.jstor.org/stable/2687673 - page 314-315).

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