IB Maths AA SL Topic 3: Geometry and trigonometry questions

A square-based right pyramid models a roof structure. The side length of its horizontal base is $4\text{ m}$ The apex $S$ is vertically above the centre $O$ of the base, and $SO=2\sqrt{2}\text{ m}$ Let $A$ be a vertex of the base.

A point moves around a circle of radius 1. Its position is described by an angle $x$ measured from the positive horizontal axis, where $0\leq x\leq 2\pi$

At one measurement, the point’s vertical coordinate is $\frac12$ At another measurement, its horizontal coordinate is $-\frac{\sqrt3}{2}$

Figure 1 shows a point $P$ on the unit circle. The angle $\theta$ is measured anticlockwise from the positive $x$-axis to $OP$ and $\theta$ lies in quadrant II.