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Find the values of other five trignometric function $\tan x=\large\frac{-5}{12}$,$x$ lies in the second quadrant

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Toolbox:
  • $\sin \theta=\large\frac{\text{opposite}}{\text{hypotenuse}}$
  • $\cos \theta=\large\frac{\text{adjacent}}{\text{hypotenuse}}$
  • $\tan \theta=\large\frac{\text{opposite}}{\text{adjacent}}$
  • $cosec \theta=\large\frac{\text{hypotenuse}}{\text{opposite}}$
  • $\sec \theta=\large\frac{\text{hypotenuse}}{\text{adjacent}}$
  • $\cot \theta=\large\frac{\text{adjacent}}{\text{opposite}}$
Since $x$ lies in second quadrant
$\tan x=\large\frac{MP}{OM}=\frac{-5}{12}=\frac{5}{-12}$
$MP=5,OM=-12$
$OP=\sqrt{MP^2+OM^2}$
$\;\;\;=\sqrt{5^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}=13$
$OP=13$
$\sin x=\large\frac{MP}{OP}=\frac{5}{13}$
$\cos x=\large\frac{OM}{OP}=\frac{-12}{13}=-\frac{12}{13}$
$cosec x=\large\frac{OP}{MP}=\frac{13}{5}$
$\sec x=\large\frac{OP}{OM}=\frac{13}{-12}=-\frac{13}{12}$
$\tan x=\large\frac{OM}{MP}=\frac{-12}{5}=-\frac{12}{5}$
answered Apr 17, 2014 by sreemathi.v
 

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