IGCSE Cosine Rule: Complete Guide for Cambridge IGCSE Mathematics

IGCSE cosine rule is an essential trigonometry topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering cosine rule formula, finding missing sides and angles, and cosine rule applications is essential for solving non-right-angled triangle problems.

This comprehensive IGCSE cosine rule guide covers everything you need to know, including the cosine rule formula, when to use it, finding missing sides, finding missing angles, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to use the cosine rule to find missing sides and angles in non-right-angled triangles, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Trigonometry practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Cosine Rule Matters

IGCSE cosine rule is an essential trigonometry topic. Here’s why it’s so important:

• High frequency topic: Cosine rule questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for solving non-right-angled triangles
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in surveying, navigation, and engineering
• Problem-solving skills: Develops trigonometry and triangle-solving abilities

Key insight from examiners: Students often confuse when to use cosine rule vs sine rule or make calculation errors. This guide will help you master these systematically.

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Understanding Cosine Rule

Cosine rule (finding side): a² = b² + c² - 2bc cos(A)

Cosine rule (finding angle): cos(A) = (b² + c² - a²) / (2bc)

Where:

• a, b, c are sides
• A is angle opposite side a

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When to Use Cosine Rule

Use when you have:

• Three sides (SSS) - to find an angle
• Two sides and included angle (SAS) - to find the third side

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Finding Missing Sides

Example 1: Triangle ABC: side b = 8 cm, side c = 10 cm, angle A = 60°. Find side a.

Solution: Using cosine rule: a² = b² + c² - 2bc cos(A) a² = 8² + 10² - 2(8)(10)cos(60°) a² = 64 + 100 - 160(0.5) a² = 164 - 80 = 84 a = √84 ≈ 9.17 cm

Answer: 9.17 cm

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Finding Missing Angles

Example 2: Triangle ABC: side a = 7 cm, side b = 9 cm, side c = 11 cm. Find angle A.

Solution: Using cosine rule: cos(A) = (b² + c² - a²) / (2bc) cos(A) = (9² + 11² - 7²) / (2 × 9 × 11) cos(A) = (81 + 121 - 49) / 198 cos(A) = 153 / 198 = 0.773 A = cos⁻¹(0.773) ≈ 39.3°

Answer: 39.3°

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Common Examiner Traps

• Formula errors - Remember: a² = b² + c² - 2bc cos(A) for sides
• Angle-side pairing - Angle A is opposite side a
• Calculation errors - Double-check arithmetic, especially with squares

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Practice Questions

Question 1

Triangle: sides 5 cm, 7 cm, included angle 45°. Find third side.

Solution: a² = 5² + 7² - 2(5)(7)cos(45°) a² = 25 + 49 - 70(0.707) a² = 74 - 49.49 = 24.51 a ≈ 4.95 cm

Answer: 4.95 cm

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Frequently Asked Questions About IGCSE Cosine Rule

What is the cosine rule?

Cosine rule: a² = b² + c² - 2bc cos(A) for finding sides, or cos(A) = (b² + c² - a²)/(2bc) for finding angles.

When do I use the cosine rule?

Use when you have three sides (SSS) or two sides and included angle (SAS).

How do I find a missing side?

Use a² = b² + c² - 2bc cos(A) where A is the included angle.

How do I find a missing angle?

Use cos(A) = (b² + c² - a²)/(2bc), then use inverse cosine.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Sine Rule: Complete Guide - Master sine rule
• IGCSE Area Rule: Complete Guide - Master area rule
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Cosine Rule with Tutopiya

Ready to excel in IGCSE cosine rule? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
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Book a free IGCSE maths trial lesson and get personalized support to master cosine rule and achieve your target grade.

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