Finding Cartesian Equations for Curves Given in Polar Coordinates
Typically a curve is given in polar coordinates
with
as a function of
It is often quite simple to write this in cartesian coordinates
by making the substitutions
and simplifying the resulting expression.
Example:
On substituting these, the equation becomes
Subtract the terms on the right hand side to give
We can complete the square for both the
's and
's to give
This is the equation of a circle with centre
and radius 2. Note that
satisfies the cartesian equation so lies on the curve.
