# Topic Questions: • understand the relationship of the secant, cosecant and cotangent functions to cosine, sine and tangent, and use properties and graphs of all six trigonometric functions for angles of any magnitude — 9709 P3 Trigonometry > 17 9709 P3 Trigonometry topic questions (45 marks) on understand the relationship of the secant… — 16 papers, 2020–2026. Open the exact question in the… - Canonical HTML: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/understand-the-relationship-of-the-secant-cosecant-and-cotangent-functions-to-cosine/ - Markdown mirror: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/understand-the-relationship-of-the-secant-cosecant-and-cotangent-functions-to-cosine/index.md --- CIE IAL · Mathematics · 9709 P3 · Trigonometry 17 9709 P3 Trigonometry topic questions are tagged to this syllabus point across 16 papers (2020–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved. - 17 topic questions - 16 papers - 45 tagged marks - 12.3% of topic questions - 8.4% of topic marks - 2020–2026 - Syllabus 2020–2027 - [All 9709 P3 Trigonometry topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/) - [All paper codes](https://www.examsci.com/topics/) Core finding **This Trigonometry syllabus point appears in 16 9709 P3 papers across 2020–2026, contributing 17 topic questions and 45 marks.** The most recent appearance is 9709/32 May/June 2026. That equals 12.3% of the 138 topic questions and 8.4% of the 536 marks tagged to Trigonometry. Only parts tagged to this subtopic are counted, so a four-part question can contribute one item and one part's marks. The table lists every matching question, its tagged parts and marks, with a link back to the paper page. Sessions are newest first, so the statement can be traced back through the full paper history. ## Topic questions by session Newest sessions first. Parts and marks count only the parts tagged to this subtopic; “x of y parts” shows how much of the question is tagged elsewhere. Select the paper cell to open the matching question on the paper page, or use **Go to Practice Hub** to answer that exact question in the Interactive Practice Hub. | Paper | Question | Type | Parts | Marks | Difficulty | Practice | | --- | --- | --- | --- | --- | --- | --- | | [**9709/32** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-may-june-9709-32/#q-7) | **Q7** Trigonometric Differentiation and Quadratic Equation - CIE A Level Mathematics 2026 June Paper 32 Q7 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d6e975a2-e88a-4b40-82f8-1078f926f377&question_id=1c1eeaee-831c-48d7-9471-7657d6741133&source_detail=9709%2F32+May%2FJune+2026) | | [**9709/32** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-may-june-9709-32/#q-8) | **Q8** Numerical Solution of Trigonometric Equation - CIE A Level Mathematics 2026 June Paper 32 Q8 | FRQ | 1 of 4 parts ((a)) | 2 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d6e975a2-e88a-4b40-82f8-1078f926f377&question_id=299f97c6-1877-4861-b87e-0f78f1778443&source_detail=9709%2F32+May%2FJune+2026) | | [**9709/32** March 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2026-march-9709-32/#q-7) | **Q7** Numerical Root Finding of Trigonometric Transcendental Equation - CIE P3 2026 Mar Q7 | FRQ | 1 of 3 parts ((a)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0fd758f5-8815-4e29-a05d-65b87156efed&question_id=ed5e5d5b-d4a5-4ab4-9ea3-81be7224752f&source_detail=9709%2F32+March+2026) | | [**9709/31** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-31/#q-9) | **Q9** Numerical Roots of Trigonometric Equation - CIE Pure Mathematics 2025 Nov Q9 | FRQ | 1 of 4 parts ((a)) | 2 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7ffa0858-5cbd-490e-9150-de28164f7cda&question_id=86a85d65-32ec-4c59-a187-65d5ab419297&source_detail=9709%2F31+October%2FNovember+2025) | | [**9709/32** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-32/#q-6) | **Q6** Trigonometric Root Location and Iterative Method - CIE A Level Maths 2025 Winter P32 Q6 | FRQ | 1 of 3 parts ((a)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d271f67a-f544-4649-81c5-cdf7c8a90ccc&question_id=6307e64f-bb21-486b-9e7d-0faf3c1c30df&source_detail=9709%2F32+October%2FNovember+2025) | | [**9709/35** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-october-november-9709-35/#q-6) | **Q6** Quotient Rule Differentiation and Stationary Points - CIE A Level Mathematics 2025 Winter Paper 35 Q6 | FRQ | 1 of 2 parts ((b)) | 2 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2b303406-630f-44c2-814e-7e47fa277f61&question_id=a973c774-6116-42f6-be63-1da739db0b3a&source_detail=9709%2F35+October%2FNovember+2025) | | [**9709/33** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-33/#q-8) | **Q8** Trigonometric Identity Proof - CIE A-Level Math 2025 Jun Paper 33 Q8 | FRQ | 1 of 2 parts ((b)) | 4 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=b947d72f-ec97-4d00-ae14-757145ba0aa9&question_id=6e100601-10b8-4627-96ee-6fbce437aa8d&source_detail=9709%2F33+May%2FJune+2025) | | [**9709/35** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2025-may-june-9709-35/#q-2) | **Q2** Trigonometric Equation in Cosecant and Cotangent - CIE A Level Mathematics | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2cdcf4cc-bb80-426a-8133-c75f6e9636f0&question_id=aab43032-e5db-46ff-87eb-956d8e5c2529&source_detail=9709%2F35+May%2FJune+2025) | | [**9709/31** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-31/#q-6) | **Q6** Numerical Solution of Equations - CIE A-Level Maths 2024 Jun Paper 31 Q6 | FRQ | 1 of 5 parts ((a)) | 2 of 9 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d001bb3e-de7a-4991-8014-a2761a618aba&question_id=44936c7c-7b6b-4876-80ca-7f775a6ddd0d&source_detail=9709%2F31+May%2FJune+2024) | | [**9709/33** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2024-may-june-9709-33/#q-7) | **Q7** Polynomial Factorization and Trigonometric Equation - CIE A-Level Pure Mathematics | FRQ | 1 of 3 parts ((c)) | 3 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7e0feb6b-4f09-4f55-8eeb-a9c09d82ec52&question_id=f8a32917-41dd-4e1c-88ce-d2d3ccf7fd60&source_detail=9709%2F33+May%2FJune+2024) | | [**9709/32** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-october-november-9709-32/#q-8) | **Q8** Area Under Curve with Substitution and Parts - CIE Pure Mathematics 2022 Nov Paper 32 Q8 | FRQ | 1 of 2 parts ((a)) | 1 of 8 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ec345ecb-a979-44f7-9e14-294a778ff934&question_id=e8635ee0-3cd1-4778-9741-dd263cb5ccb7&source_detail=9709%2F32+October%2FNovember+2022) | | [**9709/31** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2022-may-june-9709-31/#q-3) | **Q3** Trigonometric Equation with Double Angle Cotangent - CIE Pure Mathematics 2022 Jun Paper 31 Q3 | FRQ | 1 part | 6 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=09685b56-86ca-46e2-9c33-353cef143122&question_id=6f38703f-3ddd-417b-912b-ef0ddf805ec0&source_detail=9709%2F31+May%2FJune+2022) | | [**9709/32** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-may-june-9709-32/#q-6) | **Q6** Trigonometric Identity and Integration - CIE 9709 2021 Jun Paper 32 Q6 | FRQ | 1 of 2 parts ((a)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=193dfa4e-69a9-4d3a-8797-abee668ebcf8&question_id=88328e0b-c724-4f96-b57b-0489850231dd&source_detail=9709%2F32+May%2FJune+2021) | | [**9709/33** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2021-may-june-9709-33/#q-6) | **Q6** Root Location and Iteration - CIE 9709 2021 Jun Paper 33 Q6 | FRQ | 1 of 3 parts ((a)) | 2 of 7 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=279950d4-e630-466e-8074-e1e13ad3f5e6&question_id=df363ea0-657e-4f22-af15-be520488ae8e&source_detail=9709%2F33+May%2FJune+2021) | | [**9709/31** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-october-november-9709-31/#q-5) | **Q5** Roots of Cosecant and Exponential Equation - CIE 9709 W20 P31 Q5 | FRQ | 1 of 2 parts ((a)) | 2 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=6d3dbf03-a763-4245-9cd4-e9bb82088912&question_id=08537ede-a29e-4b84-8739-a31228faded4&source_detail=9709%2F31+October%2FNovember+2020) | | [**9709/33** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-october-november-9709-33/#q-5) | **Q5** Numerical Solution of Equations - CIE Pure Mathematics 2020 Nov Paper 33 Q5 | FRQ | 1 of 2 parts ((a)) | 2 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=086627cb-e617-484f-abc7-431aab41e928&question_id=7b28be74-f813-4570-95a1-d589b529c6bf&source_detail=9709%2F33+October%2FNovember+2020) | | [**9709/32** March 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p3/2020-march-9709-32/#q-3) | **Q3** Root Location and Iteration - CIE Pure Mathematics 3 March 2020 Q3 | FRQ | 1 of 3 parts ((a)) | 2 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11f225a5-63c6-446a-9114-463175a53c07&question_id=1ecf2783-e374-4d34-b0be-071055cfd079&source_detail=9709%2F32+March+2020) | ## Related topic questions in Trigonometry - [• use trigonometrical identities for the simplification and exact evaluation of expressions, and in the course of solving equations, and select an identity or identities appropriate to the context, showing familiarity in particular with the use of – $\sec^2\theta\equiv1+\tan^2\theta$ and $\operatorname{cosec}^2\theta\equiv1+\cot^2\theta$ – the expansions of $\sin(A\pm B)$, $\cos(A\pm B)$ and $\tan(A\pm B)$ – the formulae for $\sin 2A$, $\cos 2A$ and $\tan 2A$ – the expression of $a\sin\theta+b\cos\theta$ in the forms $R\sin(\theta\pm\alpha)$ and $R\cos(\theta\pm\alpha)$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/use-trigonometrical-identities-for-the-simplification-and-exact-evaluation-of/) — 104 question items · 42 papers — 440 marks · 2020–2026 ## Topic question rules and edge cases **How many topic questions cover this syllabus point?** 17 question stems cover this subtopic across 16 papers, but only 17 tagged parts and 45 marks belong to it. Other parts of the same questions are assessed under different statements and are excluded from this page. **Which papers include this subtopic?** The table lists every matching session from 2020–2026. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available. **Why can one question appear under several subtopics?** The parts of one question can assess different syllabus statements. Each part is counted under its own subtopics, so the same question stem can appear on several subtopic pages while each page lists only the parts and marks tagged to that statement. **Can I practise these questions with AI marking?** Yes. Open a paper from the table and use the Interactive Practice Hub entry point. The page itself is static HTML so search engines and retrieval agents can read the full question list without executing JavaScript. --- Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/cie-ial/mathematics/9709-p3/trigonometry/understand-the-relationship-of-the-secant-cosecant-and-cotangent-functions-to-cosine/