IB Maths AA SL Topic 3: Geometry and trigonometry questions

During map-making, a survey team records three landmarks, $P$ $A$ and $B$ The distances $PA$ and $PB$ are $8.0\text{ km}$ and $11.0\text{ km}$ respectively, and $\angle APB=60.0^\circ$

Give your answers to three significant figures.

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.

In triangle $ABC$ angles $A,B,C$ are measured in degrees. Using the usual notation for sides opposite the corresponding angles, $A=30^\circ$ $a=6\text{ cm}$ and $b=9\text{ cm}$

A Ferris-wheel passenger’s height above the ground, $h$ metres, $t$ minutes after the ride begins is modelled by

where $a,b>0$ and $0\leq c<\frac{2\pi}{b}$

The passenger’s lowest and highest heights are $3$ m and $15$ m respectively. The wheel reaches its highest point at $t=2$ its lowest point at $t=8$ and its next highest point at $t=14$

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 $-\frac{\sqrt3}{2}$

For $0\leq x<2\pi$ let $f(x)=2\sin^2x+3\cos x-1$

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.