Tangent machine. Animation showing the relationship between a circle (wheel) and a tangent (green). The tangent of a curve is a straight line that just touches the curve, but does not intersect it. The rod that traces the tangent is an extension of the wheel's diameter. As the wheel rotates, it insects a plane (purple) and traces the tangent. When the rod is completely vertical it is not intersecting the graph and tan is equal to infinity. Subsequent rotation leads to a negative value of tan.