Polar and Cartesian coordinatesAQA A-Level Further Maths: Mind map

Exam questions on Polar and Cartesian coordinates

1. The point $P$ has polar coordinates $\left(4,\dfrac{5\pi}{6}\right)$.
   The point $P'$ is the reflection of $P$ in the initial line. Give the polar coordinates of $P'$ with $r>0$ and $-\pi<\theta\le\pi$.2 marks
2. The point $R$ has Cartesian coordinates $\left(-\sqrt3,-1\right)$.
   The point $R$ is rotated through $\frac{\pi}{2}$ anticlockwise about the origin. Find the Cartesian coordinates of its new position.2 marks
3. Two curves are given. Curve $C$ has Cartesian equation $x^2+y^2=4x$ and curve $D$ has polar equation $r^2=18\sin2\theta$.
   Show that $C$ has polar equation $r=4\cos\theta$.3 marks