Sine and Cosine Rule

Summary

The Sine Rule and Cosine Rule are used to solve problems involving any triangle, not just right-angled ones.

• Sine Rule — relates the sides and angles of a triangle using the sine function. Example: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
• Cosine Rule — relates the lengths of the sides of a triangle to the cosine of one of its angles. Example: $c^2 = a^2 + b^2 - 2ab \cos C$

Exam Tips

Key Definitions to Remember

• Sine Rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
• Cosine Rule: $c^2 = a^2 + b^2 - 2ab \cos C$

Common Confusions

• Confusing when to use the Sine Rule versus the Cosine Rule
• Mixing up the formulas for the Sine and Cosine Rules

Typical Exam Questions

• Given two sides and an angle, find the unknown side using the Cosine Rule? Use $c^2 = a^2 + b^2 - 2ab \cos C$ to find the side
• Given two angles and one side, find the unknown side using the Sine Rule? Use $\frac{a}{\sin A} = \frac{b}{\sin B}$ to find the side
• Find the measure of an angle in a triangle using the Sine Rule? Use $\frac{a}{\sin A} = \frac{b}{\sin B}$ to find the angle

What Examiners Usually Test

• Ability to choose the correct rule based on given information
• Correct application of the Sine and Cosine Rules
• Solving for unknown sides or angles in non-right-angled triangles