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