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Trigonometry, SMB-014

Express `cos theta` as a fraction in its simplest form.  (3 marks)

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`cos theta = sqrt3/2`

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`text{Let unknown side =}\ x`

`text{By Pythagoras:}`

`4^2` `=x^2 + 2^2`  
`x^2` `=16-4`  
`x` `=sqrt12\ \ (x>0)`  

 

`:.cos theta` `=sqrt12/4`  
  `= (2sqrt3)/4`  
  `= sqrt3/2`