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?
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.