Parametric Equations and Vectors

In BC calculus the only application parametric equations and vectors is motion in a plane. Polar equations concern area and the meaning of derivatives. See the review notes for more detail and an outline of the topics. (only 3 items here) Motion Problems: Same Thing Different Context (11-16-2012) Implicit Differentiation of Parametric Equations (5-17-2014) A…

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…

February 2016

As I hope you’ve noticed there is a new pull-down on the navigation bar called “Website.” For some years I’ve had a website at linmcmullin.net that lately I’ve been neglecting. I decided to close it in the next few days, and therefore, I move most of the material that is there to this new tab. The…

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…

Roulettes and Art – 1

For the last few post we have been exploring roulettes using the roulette generator (RG) for either Winplot or Geometer’s Sketchpad. These files use the equations      The derivative is given by the equations Notice that the derivative is also a form of roulette. To generate various roulettes by changing the values of R…