Cosine Rule

Summary and Exam Tips for Cosine Rule

The Cosine Rule is a subtopic of Trigonometry, which falls under the subject Mathematics in the Cambridge IGCSE curriculum. It is a crucial tool for solving problems involving triangles that are not right-angled. The Cosine Rule is particularly useful in two scenarios: when you know two sides and the included angle (SAS), or when you know all three sides (SSS). The rule is mathematically expressed as:

$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$

where $c$ is the side opposite angle $C$, and $a$ and $b$ are the other two sides. This formula allows you to calculate the length of a side or the measure of an angle in a triangle. Additionally, the Cosine Rule can be combined with the Sine Rule to solve more complex problems involving unknown sides or angles. Understanding how to apply these rules is essential for solving various trigonometric problems effectively.

Exam Tips

• Understand the Formula: Make sure you can derive and apply the Cosine Rule formula: $c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$. Practice using it in different scenarios.
• Identify the Scenario: Determine whether you are dealing with an SAS or SSS situation to decide when to use the Cosine Rule.
• Combine with Sine Rule: Be prepared to use the Sine Rule in conjunction with the Cosine Rule for problems involving both unknown sides and angles.
• Practice Problems: Work through practice questions and past paper problems to become comfortable with the application of the rule.
• Check Your Work: Always double-check your calculations, especially when dealing with angles and side lengths, to avoid common errors.