Polar coordinates and curve sketchingEdexcel International A Level Further Maths: Mind map

Exam questions on Polar coordinates and curve sketching

1. The straight line $l$ has polar equation $r=4\sec\left(\theta-\frac{\pi}{3}\right)$, where $r\ge0$ and the pole is $O$.
   Find the polar coordinates of the point where $l$ meets the initial line.2 marks
2. The curve $S$ has polar equation $r=3\theta$, for $\theta\ge0$.
   Find the Cartesian coordinates of the point on $S$ where $\theta=\frac{3\pi}{2}$.2 marks
3. The curve $C$ has polar equation $r=3+2\cos\theta$, for $0\le\theta<2\pi$.
   Find the greatest and least values of $r$, stating the value of $\theta$ at each, and explain why $C$ does not pass through the pole.3 marks