the Further Mathematics network

the Further Mathematics network FP2 (MEI) Polar coordinates and curves, the area of a sector Let Maths take you Further…

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 Use the graph y=4cosx to help Sketch on polar paper the graph of

rhodonea

Autograph Demonstration 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.