IB Maths AA SL 3.5 Unit circle and exact values Question Bank

Practise IB Mathematics SL/HL 3.5 by applying unit circle and exact values methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 5]

The following diagram shows a straight shoreline, with a supply store at S , a town at T , and an island L .

Figure for Question SL 3.5—Unit circle and exact values question 1 — IB Maths AA SL

A boat delivers supplies to the island. The boat leaves S , and sails to the island. Its path makes an angle of $20^{\circ}$ with the shoreline.

It is decided to change the position of the supply store, so that its distance from L is 5 km . The following diagram shows the two possible locations P and Q for the supply store.

Find the size of $S \hat{P} L$ and of $S \hat{Q} L$ .

evidence of choosing sine rule
eg $\quad \frac{\sin A}{a}=\frac{\sin B}{b}, \sin \theta=\frac{(\mathrm{SL}) \sin 20^{\circ}}{5}$
correct substitution
eg $\quad \frac{\sin \theta}{9}=\frac{\sin 20^{\circ}}{5}$
37.9981
$\mathrm{S} \hat{\mathrm{PL}}=38.0^{\circ}$
recognition that second angle is the supplement of first
eg 180-x
142.001
$\mathrm{SQL}=142^{\circ}$

All question bank results loaded

SL 3.5—Unit circle and exact values question 1