Sketching polar curvesAQA A-Level Further Maths: Mind map

Exam questions on Sketching polar curves

1. A curve $C$ has polar equation $r=4(1+\cos\theta)$ for $0\le\theta<2\pi$.
   Explain why $C$ is symmetrical about the initial line, and find the value of $r$ when $\theta=\frac{\pi}{2}$.2 marks
2. A curve $C$ has polar equation $r=3\cos2\theta$ for $0\le\theta<2\pi$.
   When $\theta=\frac{\pi}{2}$, $r$ is negative. Find the Cartesian coordinates of the point on $C$ with $\theta=\frac{\pi}{2}$.2 marks
3. A curve $C$ has polar equation $r=2+3\cos\theta$ for $0\le\theta<2\pi$.
   Find the values of $\theta$ at which $C$ passes through the pole.3 marks