The points A and B have polar coordinates  $\left(6,\ -\frac{\pi}{3}\right)\ and\ \left(8,\frac{\pi}{6}\right)\$  respectively.

OQPR is a rhombus, where Q and R have polar coordiantes $\left(2,\frac{2\pi}{3}\right)\ and\ \left(2,0\right)$ respectively and O is the pole.  The polar coordinates of P are

The polar coordinates of P are $\left(4,\frac{\pi}{4}\right)$  The pole,O, is the midpoint of the line PQ.

The Cartesian coordinates of Q are

A and B are the points of intersection of the line $r=\operatorname{cosec}\theta\ \$ and the circle  $r=4\cos\theta$  . O is the pole. 

The size of angle AOB, in radians,

 is

The radius of the circle with polar equation $r=6\cos\theta-2\sin\theta$ 

is