Polar Coordinates (Edexcel A-Level Further Mathematics): Flashcards

$x = r \cos \theta$, $y = r \sin \theta$

$r = \sqrt{x^2 + y^2}$

$\theta = \tan^{-1}(\frac{y}{x})$

$r = a$

$r = a(1 \pm \cos \theta)$ or $r = a(1 \pm \sin \theta)$

Heart-shaped curve

$r = a \cos n\theta$ or $r = a \sin n\theta$

$n$ petals if $n$ odd, $2n$ petals if $n$ even

$r^2 = a^2 \cos 2\theta$

$r = k\theta$