CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 10. Polar and Parametric Equations

10.4 Parametric Inverses

Here you will use your knowledge of both inverses and parametric equations to solve problems.
You have learned that a graph and its inverse are reflections of each other across the liney=x.You have also
learned that in order to find an inverse algebraically, you can switch thexandyvariables and solve fory.Parametric
equations actually make finding inverses easier because both thexandyvariables are based on a third variablet.All
you need to do to find the inverse of a set of parametric equations and switch the functions forxandy.
Is the inverse of a function always a function?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/62006

http://www.youtube.com/watch?v=4Y14XhPD7Os James Sousa: Graphing Parametric Equations in the TI84

Guidance

To find the inverse of a parametric equation you must switch the function ofxwith the function ofy.This will switch
all the points from(x,y)to(y,x)and also has the effect of visually reflecting the graph over the liney=x.
Example A
Find and graph the inverse of the parametric function on the domain− 2 <t< 2.

x= 2 t

y=t^2 − 4

Solution:Switch thexandyfunctions and graph.

x=t^2 − 4

y= 2 t

The original function is shown in blue and the inverse is shown in red.