Unit 3: Geometry and Trigonometry
Topic 3.5: The Unit Circle Questions
Practice 14 exam-style questions for IB Math AA SL Topic 3.5. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find2 marks
2026• Aimnova practice — 3.5.2
An angle x in a triangle has sin x = sin 64°, with x obtuse. Find x.
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2026• Aimnova practice — 3.5.1
Write down the exact value of sin 90° and cos 90°.
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2026• Aimnova practice — 3.5.1
Write down the exact value of (a) cos 60° and (b) tan 45°.
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2026• Aimnova practice — 3.5.1
Given that sin θ = sin 50° and 90° < θ < 180°, find θ.
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2026• Aimnova practice — 3.5.2
An angle θ in a triangle satisfies sin θ = 0.8. Find both possible values of θ, to 3 s.f.
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2026• Aimnova practice — 3.5.2
In triangle ABC, A = 80°, the sine rule gives B ≈ 45° or 135°. Determine which value(s) of B are possible, with a reason.
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2026• Aimnova practice — 3.5.1
Given that cos θ = 3/5 and θ is acute, find the exact value of sin θ.
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2026• Aimnova practice — 3.5.1
Given sin θ = 5/13 and θ is acute, find the exact value of cos θ.
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2026• Aimnova practice — 3.5.2
Explain why using the cosine rule to find an angle never gives an ambiguous (two-answer) result.
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2026• Aimnova practice — 3.5.1
State the sign (positive or negative) of (a) cos 200° and (b) sin 300°. Give the quadrant in each case.
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2026• Aimnova practice — 3.5.2
In triangle ABC, A = 30°, a = 5 and b = 8. (a) Find both possible values of B. (b) For each, find the corresponding value of angle C.
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2026• Aimnova practice — 3.5.2
In triangle ABC, A = 35°, a = 10 and b = 14. Find both possible values of angle B, to 3 s.f.
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2026• Aimnova practice — 3.5.1
Given that cos θ = −3/5 and 90° < θ < 180°, find the exact value of sin θ.
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2026• Aimnova practice — 3.5.2
In triangle PQR, P = 28°, p = 8 and q = 15. (a) Find sin Q. (b) Hence find both possible values of Q, to 3 s.f.
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