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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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Find the values of other five trignometric function $\cos x=-\large\frac{1}{2}$,$x$ lies in the third quadrant

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  • $\sin \theta=\large\frac{\text{opposite}}{\text{hypotenuse}}$
  • $\cos \theta=\large\frac{\text{adjacent}}{\text{hypotenuse}}$
  • $\tan \theta=\large\frac{\text{opposite}}{\text{adjacent}}$
  • $cosec \theta=\large\frac{\text{hypotenuse}}{\text{opposite}}$
  • $\sec \theta=\large\frac{\text{hypotenuse}}{\text{adjacent}}$
  • $\cot \theta=\large\frac{\text{adjacent}}{\text{opposite}}$
$\cos x=-\large\frac{1}{2}$
$\Rightarrow \large\frac{OM}{OP}=-\frac{1}{2}$
$\therefore OM=-1,OP=2$
$MP=-\sqrt{OP^2-OM^2}=-\sqrt{4-1}=-\sqrt{3}$
$\sin x=\large\frac{MP}{OP}=-\frac{\sqrt 3}{2}$
$\tan x=\large\frac{MP}{OM}=\frac{-\sqrt 3}{-1}$$=\sqrt 3$
$cosec x=\large\frac{OP}{MP}=-\frac{2}{\sqrt 3}$
$\sec x=\large\frac{OP}{OM}$$=-2$
$\cot x=\large\frac{OM}{MP}=\frac{-1}{-\sqrt 3}=\frac{1}{\sqrt 3}$
answered Apr 16, 2014 by sreemathi.v
 

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