Unit 3: Geometry and Trigonometry

Topic 3.11: Trig relationships (HL only) Questions

Practice 11 exam-style questions for IB Math AA SL Topic 3.11. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Prove2 marks
2026
Prove the identity cot x · sin x = cos x.
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21 mark
2026
sec θ is defined as:
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31 mark
2026
Which identity is obtained by dividing sin²θ + cos²θ = 1 by cos²θ?
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41 mark
2026
1 + tan²θ equals:
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51 mark
2026
Simplify sin θ · csc θ.
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61 mark
2026
Which is the correct co-function relationship?
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7Find3 marks
2026
Given that θ is acute with sin θ = 5/13, find the exact values of csc θ and cot θ.
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8Show3 marks
2026
Show that (1 − cos²x) csc x = sin x.
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9Express3 marks
2026
Write 3sec x − 2cos x as a single fraction in terms of cos x.
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10Simplify2 marks
2026
Simplify (1 + cot²x) sin²x.
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11Find4 marks
2026
Consider f(x) = 2cot x + sin x for 0 < x < π.
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