IB Maths AA HL 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.

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Find the value of $\sin \frac{\pi}{4}+\sin \frac{3 \pi}{4}+\sin \frac{5 \pi}{4}+\sin \frac{7 \pi}{4}+\sin \frac{9 \pi}{4}$ .

$\quad \sin \frac{\pi}{4}+\sin \frac{3 \pi}{4}+\sin \frac{5 \pi}{4}+\sin \frac{7 \pi}{4}+\sin \frac{9 \pi}{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$
Note: Award M1 for 5 equal terms with + or - signs.

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IB Maths AA HL Sl 3 5 Unit Circle and Exact Values Questions question 1