Topic explanation
Exact Trigonometric Values is part of the Geometry & Measures strand in GCSE Maths. Sin, cos and tan for 0°, 30°, 45°, 60°, 90° without a calculator — exact answer forms.
Exam papers from AQA, Edexcel, OCR assess fluency (short questions) and reasoning (multi-mark). Practise reading command words (“show that”, “hence”, “give your answer in the form…”) before you rearrange algebra or interpret a result.
Key formulas & rules
- Pythagoras: a² + b² = c² (right-angled triangles)
- SOHCAHTOA for right-angled trig; sine/cosine rules for non-right triangles
- Circle: circumference 2πr; area πr²; volume formulas for prisms, cylinders, cones, spheres
Common mistakes
- Arithmetic and sign errors when simplifying expressions involving exact trigonometric values.
- Not answering in the required form (fraction vs decimal, surd vs rounded).
- Missing a final sentence that interprets the result in context when the question is applied.
Exam tips
- Underline key words in the question: “exact”, “integer”, “give reasons”.
- Estimate or use inverse operations to sanity-check answers when a calculator is allowed.
- Use StudyVector practice filtered to “SOHCAHTOA Problems” to drill exam-style questions on this skill.
Practice questions
Exam-style questions aligned to your board. Open full practice for worked feedback and your next best question.
No preview items in the bank for this match yet — jump into practice to pull from the full GCSE Maths set.