Introduction
The cosine rule is one of the most important formulas in the IB Math syllabus. Found in the IB Math formula booklet, it is essential for solving problems involving non-right-angled triangles. While many students are comfortable with trigonometry in right-angled triangles, the cosine rule expands these ideas, allowing you to handle more complex geometry problems.
Both IB Math Analysis and Approaches (AA) and Applications and Interpretation (AI) students must use the cosine rule, and it frequently appears in Paper 1 and Paper 2 questions. In HL exams, the cosine rule often combines with vectors or calculus to create multi-step challenges.
Quick Start Checklist
To use the cosine rule effectively:
- Memorize the formula: c² = a² + b² – 2ab cos C.
- Know when to apply it (non-right-angled triangles).
- Practice both “finding a side” and “finding an angle.”
- Watch out for ambiguous cases (like obtuse triangles).
- Pair with the sine rule when necessary.
The Formula Explained
The cosine rule appears in the IB Math booklet as:
c² = a² + b² – 2ab cos C
Where:
- a, b, c are sides of a triangle.
- C is the angle opposite side c.
Variations include:
- a² = b² + c² – 2bc cos A
- b² = a² + c² – 2ac cos B
This symmetry means you can solve for any side or angle as long as you know two sides and one angle, or all three sides.
