1.1. Figure 1 shows a sketch of a Ferris wheel.

The Ferris wheel is modelled as a circle in the $x$-$y$ plane, with centre $(0,0)$ and radius exactly $60$ m.

According to the model,

• there are exactly $30$ passenger pods evenly spaced around the Ferris wheel

• the position of a passenger pod can be determined by the angle $\theta$ radians, measured anticlockwise from the positive $x$-axis, as shown in Figure 1

• the coordinates $(x,y)$ of a passenger pod are given by

$(x,y)=(A\text{cos} \theta ,B\text{sin} \theta )$

where $A$ and $B$ are positive constants

• ground level is represented by the horizontal line with equation $y=-62$

(i) Write down the value of $A$ and the value of $B$.

(ii) Find the exact angle, in radians, between adjacent passenger pods.

1.2. Find the height above the ground of a passenger pod when $\theta =\frac{7 \pi }{6}$.

1.3. Find, to 3 significant figures, the value of $\theta$ for a passenger pod located at the point $(48,-36)$.

1.4. Evaluate the model in the case where $A\neqB$, giving a reason for your answer.