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I'm trying to understand in a practical/graphical view the derivative of $\sin(x)$ (that results in $\cos(x)$).

Is there any animation or illustration explaining that?

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    A related question: [Intuitive understanding of the derivatives of $\sin x$ and $\cos x$](http://math.stackexchange.com/q/392)2012-07-18

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MIT OCW's single variable calculus course has a interactive mathlet explaining the derivates of sines and cosines (and few others) graphically. Please refer to the worked example at here.

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    Wondeful! By the way, I think you mean "refer to the Mathlet". Thanks!2012-07-18
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Think in polar coordinates.

Draw a circle centered at the origin. Pick an angle $\theta$ on the circle. Draw a ray between the origin and the circle with that angle.

Draw the tangent line on the circle there.

Now, draw a line through the origin parallel to that tangent line. Where does it intersect the circle? At exactly $\cos(\theta)$.

This works because the tangent line on the circle is normal to the ray leading to that point. That means that the line we draw through the origin also intersects that ray at right angles.