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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$
$\cot x=\large\frac{OM}{MP}=\frac{-1}{-\sqrt 3}=\frac{1}{\sqrt 3}$