Polar Graphs and Areas (AQA A-Level Further Maths): Flashcards

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Polar Graphs and Areas
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In polar coords, what does rr represent?

Distance from the origin (the pole)

In polar coords, what does θ\theta represent?

Angle measured anticlockwise from positive x-axis

General form of cardioid curves

r=a(1+cosθ)r = a(1 + \cos\theta) or r=a(1+sinθ)r = a(1 + \sin\theta)

Max value of rr for cardioid r=a(1+cosθ)r = a(1 + \cos\theta)

2a2a

Min value of rr for cardioid r=a(1+cosθ)r = a(1 + \cos\theta)

00

Number of loops in rose curve r=acos(nθ)r = a\cos(n\theta)

nn loops

Area formula for polar sector between θ=a\theta = a and bb

A=12abr2dθA = \frac{1}{2}\int_a^b r^2 d\theta

Units required for θ\theta in polar area formula

Radians

Identity for sin2(x)\sin^2(x)

1cos(2x)2\frac{1 - \cos(2x)}{2}

Identity for cos2(x)\cos^2(x)

1+cos(2x)2\frac{1 + \cos(2x)}{2}

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