Unit 3: Geometry and Trigonometry
Topic 3.5: The Unit Circle Questions
Practice 20 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.
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Why does finding an angle with the cosine rule never give two possible answers?
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An angle θ in a triangle satisfies sin θ = 0.35. Give both values θ could have, to 3 s.f.
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Write down the exact value of (a) cos 60° and (b) tan 45°.
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Write down the exact value of (a) and (b) .
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An angle x in a triangle has , with x obtuse. Find x.
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Without using a calculator, write down the exact value of cos 30°.
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Write down the exact value of and .
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The angle 214° lies in which quadrant, and what are the signs of sin 214° and cos 214°?
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An angle θ satisfies sin θ = sin 72°, and θ lies between 90° and 180°. Work out θ.
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An angle x in a triangle has sin x = sin 64°, with x obtuse. Find x.
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Write down the exact value of sin 90° and cos 90°.
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In triangle ABC, angle A = 110°, and the sine rule gives angle B as 34.0° or 146°. Determine which values of B are possible.
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State the sign (positive or negative) of (a) and (b) . Give the quadrant in each case.
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An angle θ in a triangle satisfies . Find both possible values of θ, to 3 s.f.
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Explain why using the cosine rule to find an angle never gives an ambiguous (two-answer) result.
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Given and θ is acute, find the exact value of cos θ.
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State the sign (positive or negative) of (a) cos 200° and (b) sin 300°. Give the quadrant in each case.
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Given that cos θ = 3/5 and θ is acute, find the exact value of sin θ.
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Given that sin θ = sin 50° and 90° < θ < 180°, find θ.
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