PreCalc PARAMETRIC PROJECT - Essay Example

Analysis: Based on the graphs obtained via TI-84 calculator, the parametric curves 3), (4), (5), (6), and (7) were each drawn completely for ‘t’ from 0 to 2π, whereas curves (2) and (8) were constructed for ‘t’ from 0 to π and for ‘t’ from 0 to π/2, respectively. Those of (9) and (10) were both established with common motional direction at a period within 0 and 2π. While parametric curves (1), (3), (4), and (8) follow a counter-clockwise uniform path of motion, parametric curve (2) moves along a non-changing clockwise direction.

On the other hand, each of the hyperbolas of parametric curves (5), (6), and (7) consists of two regions that reflect each other’s opposite courses of motion (clockwise and counter-clockwise).Apparently, a parametric motion is governed by equations where a third variable ‘t’, known as the parameter, is introduced. One discovers and comprehends that, in dealing with problems involving parametric motion, the concept of working with parametric equations is quite impressive in the sense that these equations are plotted as a single graph designed to illustrate movement along the ‘x’ and movement along the ‘y’ (Dawkins).

To this extent, there emerges clearer understanding of the motion of a point particle as it occurs in two dimensions simultaneously. No wonder parametric motion has been applied widely in kinematics or in other similar fields that require the scheme of observing point particles in terms of their displacements, velocities, and elapsed time (t) of travel. As such, a typical kinematic problem is parametrically characterized by a projectile whose parabolic (or semi-elliptical) trajectory depicts the object’s velocity and displacement (on 2-D xy-plane) as a function of time.

Work CitedDawkins, Paul. “Parametric Equations and Curves.” Paul’s Online Math Notes. 2003 – 2014. Web. 13 May 2014. http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx.