# Find the values of other five trignometric function $\cot x=\large\frac{3}{4}$,$x$ lies in the third quadrant

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• $\sin \theta=\large\frac{\text{opposite}}{\text{hypotenuse}}$
• $\cos \theta=\large\frac{\text{adjacent}}{\text{hypotenuse}}$
• $\tan \theta=\large\frac{\text{opposite}}{\text{adjacent}}$
• $cosec \theta=\large\frac{\text{hypotenuse}}{\text{opposite}}$
• $\sec \theta=\large\frac{\text{hypotenuse}}{\text{adjacent}}$
• $\cot \theta=\large\frac{\text{adjacent}}{\text{opposite}}$
$\cot x=\large\frac{3}{4}$
$\Rightarrow \large\frac{OM}{OP}=\frac{3}{4}=\frac{-3}{-4}$
$\therefore OM=-3,OP=-4$
$OP=\sqrt{(-3)^2+(-4)^2}$
$\Rightarrow \sqrt{9+16}=\sqrt{25}=5$
$\sin x=\large\frac{MP}{OP}=-\frac{4}{5}$
$\cos x=\large\frac{OM}{OP}=-\frac{3}{5}$
$\tan x=\large\frac{MP}{OM}=\frac{-4}{-3}=\frac{4}{3}$
$cosec x=\large\frac{OP}{MP}=\frac{5}{-4}=-\frac{5}{4}$
$\sec x=\large\frac{OP}{OM}=\frac{5}{-3}=-\frac{5}{3}$