1.4 Parametric EquationsGreg Kelly, Hanford High School, Richland, WashingtonPhoto by Greg Kelly, 2005Mt. Washington Cog Railway, NH
There are times when we need to describe motion (or a curve) that is not a function.We can do this by writing equations for the x and y coordinates in terms of a third variable (usually tor ).xftyg tThese are calledparametric equations.“t” is the parameter. (It is also the independent variable)
Example 1:0xtyttTo graph on the TI-89:MODEGraph…….2ENTERPARAMETRICY=xt1tyt1t2ndT)ENTERWINDOWGRAPH
Hit zoom square to see the correct, undistorted curve.We can confirm this algebraically:xtytxy2xy0x2yx0xparabolic function
tCircle:If we let t= the angle, then:cos sin 02xtytt Since:22sincos1tt221yx221xyWe could identify the parametric equations as a circle.
Graph on your calculator:Y=xt1cos( )tyt1sin( )tWINDOWGRAPH2Use a [-4,4] x [-2,2] window.