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Coursework Notes - Shape & Space

 

Sine & Cosine Rules

 

the Sine Rule

the Cosine Rule

 

 

The Sine Rule

 

 

sine rule

 

Method

 

      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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