A Level Maths Notes: FP1 – Finding the Turning Points of Polar Curves
A turning point in cartesian coordinates is the solution to
We
cannot form this expression in polar coordinates directly. If in
polar coordinates we have
as
a function of
then
and
so
now
and
are
expressed in terms of the angle
and
we can use the parametric formula for the gradient
to
find the gradient at any point.
If we want a turning point then we solve
From
this we obtain value(s) for
and
can then use
to
obtain values for
Example
Find
the turning point.
Clear all the factions by multiplying by
and
cancel the non zero constant
obtaining
Divide throughout by
to
obtain
Now use the double angle formula
to
express everything in terms of
Clear all the fractions to obtain