Sine and Cosine Rule Equations

equations needed for Sine and Cosine rule topic in edexcel C2

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Sine Rule

Basic Rule

  • a = b = c
    sin A sin B sin C
  • sin A = sin B = sin C
    a b c

Finding the length of a side

  • a = b
    sin A sin B
  • a = c
    sin A sin C
  • b = c
    sin B sin C

Finding an angle

  • sin A = sin B
    a b
  • sin A = sin C
    a c
  • sin B = sin C
    b c

Two Solutions

  • when the angle you are finding is larger than the given angle
  • sin (180-x) = sin x
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Cosine Rule

Basic Rule

  • a^2 = b^2 + c^2 - 2bc cos A
  • cos A = b^2 + c^2 - a^2
    2bc

Finding an unknown side

  • a^2 = b^2 + c^2 - 2bc cos A
  • b^2 = a^2 + c^2 - 2bc cosB
  • c^2 = a^2 + b^2 - 2bc cosC

Finding an unknown angle

  • cos A = b^2 + c^2 - a^2
    2bc
  • cos B = a^2 + c^2 - b^2
    2bc
  • cos C = a^2 + b^2 - c^2
    2bc
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What To Use and When?

Right- angled or isosceles

  • sine theorem (sin A = a/b)
  • cosine theorem (cos A = c/b)
  • tangent theorem (tan A = a/c)
  • Pythagoras' theorem (a^2 + b^2 = c^2)

Two sides and the included angle

  • cosine rule

Other combinations

  • sine rule
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Area of a Triangle

Basic Rule

  • 1/2 ab sin C
  • 1/2 ac sin B
  • 1/2 bc sin A
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