Type 8: Parametric and Vector Questions

The parametric/vector equation questions only concern motion in a plane. In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations  or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement…

Parametric and Vector Equations

In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations  or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement in the x- and y-direction is given by the vector . The vector…

Implicit Differentiation and Inverses

Implicit differentiation of relations is done using the Chain Rule.  Implicit Differentiation (from last Friday’s post. I discovered I never did a post on this topic before!) Implicit differentiation of parametric equations A Vector’s Derivative The inverse series  This series of posts reviews and expands what students know from pre-calculus about inverses. This leads to…

A Vector’s Derivatives

A question on the AP Calculus Community bulletin board this past Sunday inspired me to write this brief outline of what the derivatives of parametric equations mean and where they come from. The Position Equation or Position Vector A parametric equation gives the coordinates of points (x, y) in the plane as functions of a…

Rolling Circles

A few weeks ago I covered some trigonometry classes for another teacher. They were studying polar and parametric graphs and the common curves limaçon, rose curves, cardioids, etc. I got to thinking about these curves. the next few posts will discuss what I learned. To help me see what was happening I made a Winplot…