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Trigonometry, 2ADV T2 SM-Bank 33

Given  `sectheta = −37/12`  for  `0 < theta < pi`,

find the exact value of  `text(cosec)\ theta`.  (2 marks)

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`37/35`

Show Worked Solution

`sec\ theta = −37/12 => cos\ theta = −12/37`
 

`text(Graphically:)`

`x=sqrt(37^2 – 12^2)=35`
 

`:.\ text(cosec)\ theta` `= 1/(sintheta)`
  `= 1/(35/37)`
  `= 37/35`

Trigonometry, 2ADV T2 SM-Bank 31

Given  `cottheta = −24/7`  for  `−pi/2 < theta < pi/2`, find the exact value of

  1.  `sectheta`  (2 marks)

  2.  `sintheta`  (1 mark)

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  1. `25/24`
  2. `-7/25`
Show Worked Solution

i.   `cot theta = −24/7\ \ =>\ \ tan theta=– 7/24`

`text(Graphically, given)\ −pi/2 < theta < pi/2:`

`x= sqrt(24^2 + 7^2)=25`
 

`sectheta` `= 1/(costheta)`
  `= 1/(24/25)`
  `= 25/24`

 

ii.   `sintheta = −7/25`