1.1. A Ferris wheel with $p$ passenger “pods” is modelled as a circle with centre $(0,0)$ and radius $50$ m.  A pod’s position can be determined by the angle,$\theta$ radians, which is measured anticlockwise from the positive $x$-direction, as shown in the diagram below.

The coordinates of a pod, $(x,y)$, are given by $(Acos( \theta ),Asin( \theta ))$ , where $A$ is a positive constant. Ground level is represented by the line with equation y=-60.

(i) Write down the value of the constant $A$.

(ii) The angle between each pod is  $\frac{ \pi }{12}$ radians. Find the value of $p$.

(iii) Find the maximum height above the ground of a passenger pod during one complete rotation of the Ferris wheel.

1.2. Find, to three significant figures, the angle $\theta$ for a passenger pod located at the point $(30,40)$.