# 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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Basic Rule

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