Parametric Equations. Dr. Dillon Calculus II Spring 2000. Introduction. Some curves in the plane can be described as functions. Others. cannot be described as functions. Example:. Ways to Describe a Curve in the Plane. An equation in two variables. This equation describes a circle.
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Some curves in the plane can be described as functions.
cannot be described as functions.
This polar equation describes a double spiral.
We’ll study polar curves later.
The “parameter’’ is t.
It does not appear in the graph of the curve!
The x coordinates of points on the curve are given by a function.
The y coordinates of points on the
curve are given by a function.
A path is a curve, together with a journey traced along the curve.
When we write
we might think of x as the x-coordinate
of the position on the path at time t
and y as the y-coordinate
of the position on the path at time t.
The path described by
is a particular route along the curve.
Path moves right!
Path moves left!
To designate one route around the unit circle use
counterclockwise from (1,0).
Think of t as an angle.
If it starts at zero, and increases to
then the path starts at t=0, where