1.1. A Ferris wheel is modelled as a circle with centre $(0,0)$ and radius $100$ m.

There are 32 passenger “pods” which are evenly spaced around the Ferris wheel.

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  $(100cos \theta ,100sin \theta )$.

(i) Find the angle, in radians, between each pod.

(ii) Find the coordinates, to one decimal place, of the first pod located anticlockwise above the positive $x$-axis.

1.2. (i) Write down the angle $\theta$ for the passenger pod located at the point $(-100,0)$.

(ii) Determine the angle $\theta$ for the pod located at the point $(50,50\sqrt{3})$.