# Topic Questions: • use the exact values of the sine, cosine and tangent of 30°, 45°, 60°, and related angles — 9709 P1 Trigonometry

> 21 9709 P1 Trigonometry topic questions (57 marks) on use the exact values of the sine, cosine and… — 14 papers, 2020–2026. Open the exact question in the…

- Canonical HTML: https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/use-the-exact-values-of-the-sine-cosine-and-tangent-of-30-45-60-and-related-angles/
- Markdown mirror: https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/use-the-exact-values-of-the-sine-cosine-and-tangent-of-30-45-60-and-related-angles/index.md

---

CIE IAL · Mathematics · 9709 P1 · Trigonometry

21 9709 P1 Trigonometry topic questions are tagged to this syllabus point across 14 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.

- 21 topic questions
- 14 papers
- 57 tagged marks
- 13.6% of topic questions
- 12.1% of topic marks
- 2020–2026
- Syllabus 2020–2027
- [All 9709 P1 Trigonometry topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**This Trigonometry syllabus point appears in 14 9709 P1 papers across 2020–2026, contributing 21 topic questions and 57 marks.** The most recent appearance is 9709/15 May/June 2026. That equals 13.6% of the 154 topic questions and 12.1% of the 471 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 |
| --- | --- | --- | --- | --- | --- | --- |
| [**9709/15** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2026-may-june-9709-15/#q-8) | **Q8** Right-Angled Triangle Angle and Length - CIE Pure Mathematics 2026 Jun Paper 15 Q8 | FRQ | 2 of 3 parts ((a), (b)(i)) | 4 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=05b20104-0aad-4794-b387-5aaa042ea528&question_id=44cd958e-c92f-454e-bc79-4a04405c9b71&source_detail=9709%2F15+May%2FJune+2026) |
| [**9709/15** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2026-may-june-9709-15/#q-12) | **Q12** Arithmetic and Geometric Progressions - CIE Pure Mathematics 2026 Jun Paper 15 Q12 | FRQ | 1 of 3 parts ((b)(ii)) | 3 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=05b20104-0aad-4794-b387-5aaa042ea528&question_id=12a415ed-1b6d-4d26-b9c6-3ade0f7ad491&source_detail=9709%2F15+May%2FJune+2026) |
| [**9709/15** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2025-may-june-9709-15/#q-9) | **Q9** Trigonometric Function Transformations and Composites - CIE A-Level Mathematics 2025 Jun Paper 15 Q9 | FRQ | 1 of 4 parts ((c)) | 4 of 13 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=ec3e11d6-9d88-4ea1-b566-ffbae1af064a&question_id=6e413a34-1c4a-4028-a72e-038e58fa2f95&source_detail=9709%2F15+May%2FJune+2025) |
| [**9709/13** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2024-october-november-9709-13/#q-2) | **Q2** Trigonometric Equation with Tan - CIE Pure Mathematics 2024 Nov Paper 13 Q2 | FRQ | 1 part | 2 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d6efe97b-7a31-419e-959f-4bf66d69ec85&question_id=08a78014-8201-456f-a1a0-a2586077f8fa&source_detail=9709%2F13+October%2FNovember+2024) |
| [**9709/11** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2024-may-june-9709-11/#q-7) | **Q7** Perimeter and Area of Circular Sector Shape - CIE Pure Mathematics 1 2024 Jun Q7 | FRQ | 1 of 2 parts ((a)) | 1 of 8 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9f870f3c-54af-497e-af82-560f2f9cab32&question_id=6111ffb7-675a-4c74-94b2-c50db1b59fa1&source_detail=9709%2F11+May%2FJune+2024) |
| [**9709/12** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2024-may-june-9709-12/#q-5) | **Q5** Arithmetic and Geometric Progressions with Trigonometry - CIE P1 2024 Jun Q5 | FRQ | 2 of 3 parts ((a), (b)(ii)) | 7 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=939f65d7-5ed8-49a6-9e7c-ff8a1346d994&question_id=329c252f-5aec-476b-875b-30cf52581c5a&source_detail=9709%2F12+May%2FJune+2024) |
| [**9709/13** May/June 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2024-may-june-9709-13/#q-2) | **Q2** Trigonometric Graph Features - CIE 9709 s24 qp 13 Q2 | FRQ | 1 of 2 parts ((b)) | 2 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a06c8091-44ae-4ff0-955a-a1f81df66b39&question_id=3a7d8035-08c4-4806-b5a9-3485f98b232e&source_detail=9709%2F13+May%2FJune+2024) |
| [**9709/12** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2023-october-november-9709-12/#q-2) | **Q2** Inverse Trigonometrical Equation - CIE 9709 P12 2023 Nov Q2 | FRQ | 1 part | 2 | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1b2438c6-7fe6-48d0-b79c-a23660af16f3&question_id=9b506bde-447a-4bd4-9c3e-e3e455e91200&source_detail=9709%2F12+October%2FNovember+2023) |
| [**9709/12** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2023-may-june-9709-12/#q-6) | **Q6** Circular Sector Arc Length and Area - CIE Math 2023 Jun Paper 12 Q6 | FRQ | 1 of 2 parts ((a)) | 2 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=e3b3cac5-d933-454f-b049-0404a2feda69&question_id=37adf722-5c46-4ad9-9872-5d22f6ed0314&source_detail=9709%2F12+May%2FJune+2023) |
| [**9709/12** October/November 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-october-november-9709-12/#q-7) | **Q7** Trigonometric Identity Proof and Solving - CIE Pure Mathematics 2022 Nov Paper 12 Q7 | FRQ | 1 of 2 parts ((b)) | 4 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=5aa651b9-e602-4095-a4ba-0681f8d6962f&question_id=3fc46b6b-a7a3-4a3c-b7d2-70efd63e9da3&source_detail=9709%2F12+October%2FNovember+2022) |
| [**9709/11** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-may-june-9709-11/#q-5) | **Q5** Area and Perimeter of Circle Segment Region - CIE 9709 s22 qp 11 Q5 | FRQ | 2 parts ((a), (b)) | 7 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=13d1cb95-4ad2-4921-a6af-70e64afc07b9&question_id=2fb18744-29d8-4a87-a269-fcbd49f56c51&source_detail=9709%2F11+May%2FJune+2022) |
| [**9709/11** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-may-june-9709-11/#q-8) | **Q8** Trigonometric Transformations and Exact Solutions - CIE 9709 s22 qp 11 Q8 | FRQ | 1 of 2 parts ((b)) | 3 of 8 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=13d1cb95-4ad2-4921-a6af-70e64afc07b9&question_id=e8f5082a-bfae-4d27-90c5-f0b737dbfd45&source_detail=9709%2F11+May%2FJune+2022) |
| [**9709/12** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-may-june-9709-12/#q-7) | **Q7** Circular Sector Area and Triangle Area - CIE P1 2022 Jun Q7 | FRQ | 1 of 2 parts ((b)) | 4 of 6 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0db3f5fb-5aad-45cf-9535-2533b5052d2e&question_id=f2ae9267-1725-4d47-8625-90f7c77bfbc2&source_detail=9709%2F12+May%2FJune+2022) |
| [**9709/12** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-may-june-9709-12/#q-12) | **Q12** Geometry of Cylindrical Pipes and Rope - CIE A-Level Maths 2021 Jun P12 Q12 | FRQ | 1 of 4 parts ((c)) | 2 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18b9b1e-0c99-4c74-9a96-27220d8ddf82&question_id=be7787b0-b1dc-47a5-b6fc-e308d8529c65&source_detail=9709%2F12+May%2FJune+2021) |
| [**9709/13** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-13/#q-7) | **Q7** Arithmetic Progression with Trigonometric Terms - CIE 9709 Nov 2020 P13 Q7 | FRQ | 1 of 2 parts ((b)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=95fd6ce4-f7e7-4fab-88ee-1c4b6760c30b&question_id=3fb296b9-b870-4a0c-948c-4d15fcd2f85f&source_detail=9709%2F13+October%2FNovember+2020) |
| [**9709/13** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-13/#q-9) | **Q9** Arc Length and Area of Intersecting Circular Sectors - CIE 9709 Nov 2020 P13 Q9 | FRQ | 1 of 3 parts ((a)) | 2 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=95fd6ce4-f7e7-4fab-88ee-1c4b6760c30b&question_id=6967e583-2ede-4801-a0f1-09adbbf05183&source_detail=9709%2F13+October%2FNovember+2020) |
| [**9709/13** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-13/#q-11) | **Q11** Circle Geometry and Tangent Properties - CIE 9709 Nov 2020 P13 Q11 | FRQ | 1 of 4 parts ((b)) | 2 of 12 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=95fd6ce4-f7e7-4fab-88ee-1c4b6760c30b&question_id=7b0aaffe-c03b-4ed3-a746-79c890ccff52&source_detail=9709%2F13+October%2FNovember+2020) |
| [**9709/13** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-may-june-9709-13/#q-8) | **Q8** Geometric and Arithmetic Progressions with Trigonometry - CIE Pure Mathematics 2020 June Paper 13 Q8 | FRQ | 1 of 3 parts ((b)(ii)) | 3 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0cc28bed-3139-4568-90b0-6474d6b8b26e&question_id=6690b461-5df1-4ad7-94af-99cd730950e1&source_detail=9709%2F13+May%2FJune+2020) |

## Related topic questions in Trigonometry

- [• find all the solutions of simple trigonometrical equations lying in a specified interval (general forms of solution are not included)](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/find-all-the-solutions-of-simple-trigonometrical-equations-lying-in-a-specified/) — 61 question items · 43 papers — 211 marks · 2020–2026
- [• sketch and use graphs of the sine, cosine and tangent functions (for angles of any size, and using either degrees or radians)](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/sketch-and-use-graphs-of-the-sine-cosine-and-tangent-functions-for-angles-of-any-size/) — 27 question items · 16 papers — 57 marks · 2020–2025
- [• use the identities $\frac{\sin\theta}{\cos\theta}\equiv\tan\theta$ and $\sin^2\theta+\cos^2\theta\equiv1$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/use-the-identities-frac-sin-theta-cos-theta-equiv-tan-theta-and-sin-2-theta-cos-2/) — 54 question items · 36 papers — 183 marks · 2020–2026
- [• use the notations $\sin^{-1}x$, $\cos^{-1}x$, $\tan^{-1}x$ to denote the principal values of the inverse trigonometric relations](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/trigonometry/use-the-notations-sin-1-x-cos-1-x-tan-1-x-to-denote-the-principal-values-of-the/) — 10 question items · 9 papers — 29 marks · 2020–2026

## Topic question rules and edge cases

**How many topic questions cover this syllabus point?**

18 question stems cover this subtopic across 14 papers, but only 21 tagged parts and 57 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-p1/trigonometry/use-the-exact-values-of-the-sine-cosine-and-tangent-of-30-45-60-and-related-angles/