the Further Mathematics network
www.fmnetwork.org.uk
the Further Mathematics network
www.fmnetwork.org.uk
FP2 (MEI)
Polar coordinates and curves,
the area of a sector
Let Maths take you Further…
Polar coordinates and curves, the area of a
sector
Before you start:
 You need to know only basic trigonometry and Pythagoras’ theorem
for this section. However, the work on the modulus-argument form of
a complex number from Further Pure 1 will be useful as similar
techniques are used here.
 You need to be able to differentiate a function defined implicitly
(Core 3 chapter 4).
 You need to be confident with all types of integration covered so far,
in particular integration of sin x and cos x (Core 3 chapter 5).
 You also need to be able to use trigonometric identities in
integration, in particular for integrating sin² x and cos² x (page 3 of
the FP2 textbook).
Polar coordinates and curves, the area of a
sector
When you have finished…
You should:
Understand the meaning of polar co-ordinates (r, θ) and
be able to convert from polar to cartesian co-ordinates
and vice-versa (page 21).
 Be able to sketch curves with simple polar equations
(pages 23 – 26).
 Be able to find the area enclosed by a polar curve
(pages 27 – 28).

Conversion between Cartesian and Polar
Coordinates
Example
Equations of curves
Curve Sketching
Sketch on polar paper
the graph of r  4 cos 
Use the graph y=4cosx to help
Sketch on polar paper
the graph of
r  4 cos 3
rhodonea
Autograph Demonstration
r  k
r  a  b cos 
r  a sin n
r  a cos n
Use the constant
controller in autograph
to determine how the
values of the constants
(a,b,n and k) effect the
curve
Area of a sector
Polar coordinates and curves, the area of a
sector
When you have finished…
You should:
Understand the meaning of polar co-ordinates (r, θ) and
be able to convert from polar to cartesian co-ordinates
and vice-versa (page 21).
 Be able to sketch curves with simple polar equations
(pages 23 – 26).
 Be able to find the area enclosed by a polar curve
(pages 27 – 28).

Independent study:


Using the MEI online resources complete the
study plan for Polar coordinates 1 and Polar
coordinates 2
Do the online multiple choice tests for these
sections and submit your answers online.