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

Read sin Î¸ and cos Î¸ from unit-circle coordinates, identify the quadrant and assign the correct signs for tan Î¸=sin Î¸/cos Î¸.
Use standard-angle values and exact surd forms to evaluate or simplify trigonometric expressions without decimal approximation.
Apply quadrant, symmetry and complementary-angle relationships to convert a given trig value into the required exact value or angle.
Analyse the two-possible-triangle case in sine-rule data, decide whether both configurations are valid and report the resulting lengths or angles.

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Study SL 3.5—Unit circle and exact values conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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
$\mathrm{SQL}=142^{\circ}$

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