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

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: 2]

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