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Trigonometry, 2ADV T2 EQ-Bank 20

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

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

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`37/35`

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`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 EQ-Bank 18

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

  1.  `sec theta`   (2 marks)

  2.  `sin theta`   (1 mark)

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a.    `25/24`

b.    `-7/25`

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a.   `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`
  

b.   `sintheta = −7/25`