Polar coordinates and polar curvesEdexcel A-Level Further Maths: Mind map

Exam questions on Polar coordinates and polar curves

1. The point $P$ has polar coordinates $\left(4,\frac{2\pi}{3}\right)$ and the point $Q$ has Cartesian coordinates $(-1,-1)$.
   Find the polar coordinates $(r,\theta)$ of $Q$, with $r>0$ and $-\pi<\theta\le\pi$.2 marks
2. The curve $C$ has polar equation $r=4\cos\theta$, for $-\frac{\pi}{2}\le\theta\le\frac{\pi}{2}$.
   The circle with polar equation $r=2$ meets $C$ at two points. Find their polar coordinates, with $r>0$.2 marks
3. The curve $C$ has polar equation $r=2(1+\cos\theta)$ for $-\pi<\theta\le\pi$.
   (i) Show that $C$ is symmetrical about the initial line. (ii) State the greatest value of $r$ and the value of $\theta$ at which it occurs.3 marks