Sine and Cosine Rule

Study Notes

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: Used when given two sides and an angle opposite one of these sides, or one side and any two angles.
• Cosine Rule — relates the lengths of the sides of a triangle to the cosine of one of its angles. Example: Used when given two sides and the included angle (SAS) or all three sides (SSS).

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

• Mixing up when to use the Sine Rule versus the Cosine Rule.
• Forgetting to use the included angle in the Cosine Rule.

Typical Exam Questions

• How do you find an unknown angle using the Sine Rule? Use the formula $\frac{a}{\sin A} = \frac{b}{\sin B}$ and solve for the angle.
• How do you find an unknown side using the Cosine Rule? Use the formula $c^2 = a^2 + b^2 - 2ab \cos C$ and solve for the side.
• What is the length of a side in a triangle given two sides and an included angle? Use the Cosine Rule to find the length.

What Examiners Usually Test

• Correct application of the Sine and Cosine Rules.
• Ability to identify which rule to use based on given information.
• Accuracy in calculations and rounding to the correct decimal place.