GCSE Maths: Trigonometry
Trigonometry is the single highest-value topic on the higher-tier paper relative to time invested. Once you can spot which rule fits which triangle, most questions follow a fixed five-step routine.
Pythagoras' theorem (a² + b² = c²) is foundation tier but appears on higher-tier papers inside compound shapes. You should be able to apply it in 2D, in 3D (finding the long diagonal of a cuboid) and to find distances between coordinate points.
SOHCAHTOA is the right-angled triangle workhorse. Label the triangle (opposite, adjacent, hypotenuse), pick the ratio, set up the equation and solve. Many students lose marks by not labelling — get into the habit even on simple questions.
Exact trig values for 0°, 30°, 45°, 60° and 90° must be memorised. They appear in non-calculator questions and in proofs. Build a small reference table and rehearse it from memory.
The sine rule (a/sin A = b/sin B) and the cosine rule (a² = b² + c² − 2bc cos A) are for non-right-angled triangles. Choose the sine rule when you have a pair (side + opposite angle); choose the cosine rule when you have two sides and the included angle, or three sides. The area formula (½ab sin C) is the third member of this family.
3D trigonometry sounds harder than it is. The trick is to identify the right-angled triangle inside the 3D shape, redraw it as a 2D triangle, label it and apply SOHCAHTOA or Pythagoras. Examiners reward students who show the 2D triangle separately.
What you'll learn
- The full Trigonometry sub-topic map and how it sits within GCSE Maths
- What examiners reward in Trigonometry questions, command word by command word
- The most common Trigonometry mistakes — and how to avoid them in your answers
- How to revise Trigonometry with notes, flashcards, exam-style questions and the AI Study Coach
- How OES generates Maths resources without using official copyrighted past papers
Who this is for
- Students revising Trigonometry as part of GCSE Maths
- Anyone retaking GCSE Maths who needs a focused review of Trigonometry
- Parents and tutors supporting Maths students on Trigonometry
Learning objectives
By the end of this topic you should be able to:
- Apply Pythagoras' theorem in 2D and 3D problems
- Use SOHCAHTOA to find missing sides and angles in right-angled triangles
- Recall exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°
- Apply the sine rule, cosine rule and the area formula ½ab sin C
- Solve 3D trigonometry problems by identifying the relevant 2D triangle
- Use bearings with trigonometry to solve navigation problems
Common mistakes
- Using sin/cos/tan in non-right-angled triangles instead of the sine or cosine rule
- Not labelling opposite/adjacent/hypotenuse before choosing SOHCAHTOA
- Forgetting that bearings are measured clockwise from north
- Using the sine rule when only two sides and the included angle are given (use cosine rule)
- Rounding too early — keep full precision until the final answer
Revision tips
- Write SOHCAHTOA in big letters at the top of every trig question to remind yourself
- Drill exact values as flashcards — non-calculator papers test these directly
- Practise distinguishing sine rule vs. cosine rule from a labelled triangle alone
- Work in surds where possible to avoid rounding errors
- Always redraw the 2D triangle for 3D problems — it doubles your method marks
How OES helps
AI Revision Notes
Concise, spec-aligned notes for every Maths topic, written to match what examiners reward.
Smart Flashcards
Adaptive Maths flashcards that prioritise the cards you keep forgetting using spaced repetition.
Exam-Style Papers
AI-generated Maths practice papers in the style of real exams — not official copyrighted past papers — with mark-scheme aware feedback.
Personal AI Study Coach
A 24/7 coach that plans every Maths session, explains anything you ask and adapts to your weakest topics.
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Frequently asked questions
Is Trigonometry on every GCSE Maths specification?
Yes. Trigonometry is a core part of the GCSE Maths specification across AQA, Edexcel and OCR. Some boards weight sub-topics slightly differently, but the content on this page maps to all three.
How long should I spend revising Trigonometry?
Most students need 4–6 focused sessions to feel confident on Trigonometry: one for the notes, one or two for flashcards, and two for exam-style questions. The AI Study Coach can build a schedule for you that fits the time you have left before the exam.
Does OES use official Maths past papers for Trigonometry questions?
No. OES does not redistribute official copyrighted past papers. We generate fresh exam-style questions in the style of real AQA, Edexcel and OCR papers, marked against the published mark scheme conventions.
What are the most common mistakes on Trigonometry questions?
Using sin/cos/tan in non-right-angled triangles instead of the sine or cosine rule Not labelling opposite/adjacent/hypotenuse before choosing SOHCAHTOA The full list — and how to avoid each — is in the "Common mistakes" section above.
Is this topic harder for higher-tier or foundation students?
Most of Trigonometry is on both tiers. Higher-tier papers add a few stretch sub-topics and more demanding command words ("evaluate", "explain in detail"). The OES content is tier-aware — questions can be generated at foundation, higher or mixed difficulty.
How do I know if I've actually understood Trigonometry, not just memorised it?
The fastest test is to attempt a fresh exam-style question and self-mark it against the mark scheme. If you can hit every mark point in your own words, you understand it. If you keep dropping the same marks, the AI Study Coach can target those gaps directly.
Where should I go next after Trigonometry?
Related topics like geometry, algebra, functions build directly on Trigonometry, so they are a strong next step. You can also drill Maths exam-style papers to combine Trigonometry with everything else you have revised.
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Revise Trigonometry with the AI Study Coach