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Coursework Notes - Shape & Space


Sine & Cosine Rules


the Sine Rule

the Cosine Rule



The Sine Rule



sine rule




      1. Use either the right, or left hand equation.


      2. You are given 3 quantities and required to work out the 4 th.



Manipulating the ratio - Take two ratios, cross multiply and rearrange to put the required quantity as the subject of the equation.



sine rule derivatives




Example #1


sine rule prob#1



sine rule prob#1




Example #2


sine rule probs #2



sine rule prob #2




Example #3


sin rule probs #3



sine rule prob#3



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The Cosine Rule



cosine rule



There are two problem types:


  • 1. You are given 2 sides + an included angle and required to work out the remaining side

  • 2. You are given all the sides and required to work out the angle.



Example #1


cosine rule prob #1



cosine rule prob #1




Example #2


cosine rule prob#3



cosine rule prob #2




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