Knowledge Organiser: The Cosine Rule
Part of Cosine Rule · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: The Cosine Rule within Cosine Rule for GCSE Mathematics. Revise Cosine Rule in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
12 questions
Recall
3 flashcards
Knowledge Organiser: The Cosine Rule
Key Terms
- SAS: Two sides and the INCLUDED angle between them
- SSS: All three sides known, no angles
- Included angle: The angle that sits BETWEEN the two known sides
- Cosine rule: Generalised version of Pythagoras for any triangle
Must-Know Facts
- Use the cosine rule when: SAS (2 sides + included angle) or SSS (all 3 sides)
- Angle A is BETWEEN sides b and c in the formula
- When A = 90°, cos 90° = 0, so it simplifies to Pythagoras
- After finding cos A, use cos⁻¹ to get the angle
- Always check: the largest angle is opposite the longest side
Key Formulas
- Find side: a² = b² + c² − 2bc cos A
- Find angle: cos A = (b² + c² − a²) ÷ 2bc
- Use when: SAS or SSS
Common Mistakes
- Wrong angle pairing: In a² = b² + c² − 2bc cos A, angle A must be opposite side a
- Sign error with −2bc cos A: If angle A is obtuse, cos A is negative, so the term becomes positive — let the calculator handle this
- Finding angle — wrong rearrangement: Use cos A = (b² + c² − a²) ÷ 2bc, then cos⁻¹ to find A
- Using cosine rule when sine rule is simpler: If you have an angle-opposite-side pair, sine rule is usually easier
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Practice Questions for Cosine Rule
Which formula is the cosine rule for finding side a?
Show that when angle A = 90°, the cosine rule reduces to Pythagoras' theorem.
Quick Recall Flashcards
12 questions on Cosine Rule — practise free
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