Comment
Share
Q)

Find the values of other five trignometric function $\sin x=\large\frac{3}{5}$,$x$ lies in the second quadrant

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