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Sine Rules

Maths: Edexcel A Level Pure Maths, topic 5.3.1

Sine and Cosine Rules

We can use the sine and cosine rules to calculate angles and lengths in triangles.

Sine rule

Sine rule

Cosine rule

Cosine rule

Labelling triangles

Labelling triangles

  • Use lowercase letters for the sides and capital letters for the angles opposite each side.
Swapping A, B and C

Swapping A, B and C

  • Note that the cosine rule can be written for the other angles too:
  • c2 = a2 + b2 - 2ab cos C
  • b2 = a2 + c2 - 2ac cos B

Test yourself on Sine Rules

  • What is asin(A) {\frac{a}{sin(A)}} equal to?

  • What is csin(C) {\frac{c}{sin(C)}} equal to?

  • Would you work out x using the sine or cosine rule?

  • Would you work out x using the sine or cosine rule?

Practise this topic for free