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.
A Level Maths Notes: FP3 – Finding Cartesian Equations for Curves Given in Polar Coordinates
Typically a curve is given in polar coordinateswithas
a function ofIt
is often quite simple to write this in cartesian coordinatesby
making the substitutionsand
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.
