IB Maths AA HL 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: 2]

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

$\quad \sin \frac{\pi}{4}+\sin \frac{3 \pi}{4}+\sin \frac{5 \pi}{4}+\sin \frac{7 \pi}{4}+\sin \frac{9 \pi}{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$
(M1)A1
Note: Award M1 for 5 equal terms with + or - signs.

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SL 3.5—Unit circle and exact values question 1