IB Maths AA SL 3.5 Unit Circle and Exact Values Questions

Practise using unit-circle coordinates, exact standard-angle values, quadrant signs and symmetry, including ambiguous sine-rule configurations.

Exam points

Use the unit circle to define sine, cosine and tangent, relating tan θ to sin θ/cos θ and identifying signs by quadrant.
Evaluate and apply exact trigonometric values for standard angles, including quadrant relationships and the valid ambiguous sine-rule case.

[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 IB Maths AA SL 3.5 Unit Circle and Exact Values Questions 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

IB Maths AA SL 3.5 Unit Circle and Exact Values Questions question 1