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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Find the values of other five trignometric function $\sec x=\large\frac{13}{5}$,$x$ lies in the fourth quadrant

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  • $\sin \theta=\large\frac{\text{opposite}}{\text{hypotenuse}}$
  • $\cos \theta=\large\frac{\text{adjacent}}{\text{hypotenuse}}$
  • $\tan \theta=\large\frac{\text{opposite}}{\text{adjacent}}$
  • $cosec \theta=\large\frac{\text{hypotenuse}}{\text{opposite}}$
  • $\sec \theta=\large\frac{\text{hypotenuse}}{\text{adjacent}}$
  • $\cot \theta=\large\frac{\text{adjacent}}{\text{opposite}}$
$\sec x=\large\frac{13}{5}$
$\Rightarrow \large\frac{OP}{OM}=\frac{13}{5}$
$OP=13,OM=5$
$MP=-\sqrt{13^2-5^2}=-\sqrt{169-25}$
$\Rightarrow -\sqrt{144}$
$\Rightarrow -12$
$MP=-12$
$\sin x=\large\frac{MP}{OP}=\frac{-12}{13}$
$\cos x=\large\frac{OM}{OP}=\frac{5}{3}$
$\tan x=\large\frac{MP}{OM}=\frac{-12}{5}$
$cosec x=\large\frac{OP}{OM}=\frac{13}{-12}=-\frac{13}{12}$
$\cot x=\large\frac{OM}{MP}=\frac{5}{-12}=-\frac{5}{12}$
answered Apr 16, 2014 by sreemathi.v
 

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