This animation from Lou Talman is a dynamic representation of the area function we introduce in the standard proof of the Fundamental Theorem of Calculus.
http://clem.mscd.edu/~talmanl/HTML/FTOC.html

This animation from Lou Talman shows how a point moving around the unit circle generates the tangent function.
http://clem.mscd.edu/~talmanl/HTML/TangentCurve.html

This animation from Lou Talman shows how the sine curve can be constructed from the definition of the sine function as the y-coordinate of a point on the unit circle.
http://clem.mscd.edu/~talmanl/HTML/SineCurve.html

This animation from Lou Talman show how a planar wave-front entering a parabolic reflector is reflected to the focus of the parabola.
http://clem.mscd.edu/~talmanl/HTML/ParabolicReflector.html

This animation from Lou Talman demonstrates the reflection property of the ellipse.
http://clem.mscd.edu/~talmanl/HTML/EllipticReflector.html

This animation from Lou Talman shows how to use the definition of ellipse to trace out such a curve
http://clem.mscd.edu/~talmanl/HTML/Ellipse_Def.html

This lovely animation from Lou Talman shows how a plane intersects a cone to form the curves traditionally known as the "conic sections," - ellipses, parabolae, and hyperbolae.
http://clem.mscd.edu/~talmanl/HTML/ConicSections.html

This animation from Lou Talman is a visual proof of the Pythagorean theorem.
http://clem.mscd.edu/~talmanl/HTML/Pythagoras.html

This animation from Lou Talman shows how a point moving around the unit circle generates the tangent function.
http://clem.mscd.edu/~talmanl/HTML/TangentCurve.html

This Quicktime animation from Lou Talman shows how the sine curve can be constructed from the definition of the sine function as the y-coordinate of a point on the unit circle.
http://clem.mscd.edu/~talmanl/HTML/SineCurve.html