A-Level Further Maths
Further Pure Mathematics B (Unit 4)
Revision Session 1
Revision Session 2
Revision Session 3
Revision Session 4
From the Specification and teaching guidance:
Polar and Rectangular Coordinates: https://www.geogebra.org/m/HDkJ9kyr
Converting Between Polar and Cartesian Coordinates
(x, y) (r, θ)
4
3
r
θ
r2 = x2 + y2
(r, θ) (x, y)
x = r cosθ
y = r sinθ
Converting Between Polar and Cartesian Coordinates
(x, y) (r, θ)
r2 = x2 + y2
(r, θ) (x, y)
x = r cosθ
y = r sinθ
Find a cartesian equation for the following:
a) r = 5
b) r2 = sin2θ,
Converting Between Polar and Cartesian Coordinates
From the Specification and teaching guidance:
Sketching Polar Curves
Sketch r = a sin(3θ)
θ 0 π/6 π/3
r
initial line
y = sin(3θ)
Sketching Polar Curves
θ 0 π/2 π 3π/2 2π
r
initial line
y = cos(θ)
Sketch r = a(1 + cos θ)
Limaçon
Dimpled
Cardioid
Convex
“Limaçon of Pascal”
“Pascal’s Snail”
(Father of the ‘famous’ Pascal)
From the Specification and teaching guidance:
Parallel and Perpendicular Tangents
Find the polar coordinates of the points on the curve r = 1 + cosθ at which the tangents are parallel to the initial line.
x = r cosθ
y = r sinθ
dx/dθ = 0
dx/dθ = 0
dx/dθ = 0
dy/dθ = 0
dy/dθ = 0
dy/dθ = 0
Vertical tangents: dx/dθ = 0
Horizontal tangents: dy/dθ = 0
Parallel and Perpendicular Tangents
x = r cosθ
y = r sinθ
Area of a sector of a polar curve
(Area of the sector of a circle = ½ r2 θ (where θ is in radians))
a
b
From the Specification and teaching guidance:
A-Level Further Maths
Further Pure Mathematics B (Unit 4)
Revision Session 1
Revision Session 2
Revision Session 3
Revision Session 4
Parallel and Perpendicular Tangents
Converting Between Polar and Cartesian Coordinates