Sine and cosine rules · Year 12

In Year 12 you learn: area = ½ab sin C.

The sine and cosine rules extend trigonometry to triangles without a right angle. Label the sides a, b, c opposite angles A, B, C. Then choose the rule that fits the information you have.

Key facts

• Sine rule: a/(sin A) = b/(sin B) = c/(sin C) (use it when you know a side and its opposite angle).
• Cosine rule for a side: a² = b² + c² − 2bc cos A (two sides and the angle between them).
• Cosine rule for an angle: cos A = (b² + c² − a²)/(2bc) (all three sides).
• Area of a triangle = ½ab sin C (two sides and the angle between them).
• Sine rule for an angle can have two answers: θ and 180° − θ.

Worked examples

Other years

• Sine and cosine rules · Year 10
• Sine and cosine rules · Year 11