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

Answer 1

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• $\sin \theta=\large\frac{\text{opposite}}{\text{hypotenuse}}$
• $\cos \theta=\large\frac{\text{adjacent}}{\text{hypotenuse}}$
• $\tan \theta=\large\frac{\text{opposite}}{\text{adjacent}}$
• $cosec \theta=\large\frac{\text{hypotenuse}}{\text{opposite}}$
• $\sec \theta=\large\frac{\text{hypotenuse}}{\text{adjacent}}$
• $\cot \theta=\large\frac{\text{adjacent}}{\text{opposite}}$

http://clay6.com/mpaimg/trig3.2-2.png

$\sin x=\large\frac{3}{5}$

$\Rightarrow \large\frac{MP}{OP}=\frac{3}{5}$

$OM=-\sqrt{5^2-3^2}$

$\Rightarrow -\sqrt{25-9}=-\sqrt{16}=-4$

$\cos x=\large\frac{OM}{OP}=-\frac{4}{5}$

$\tan x=\large\frac{MP}{OM}=\frac{3}{-4}=-\frac{3}{4}$

$cosec x=\large\frac{OP}{MP}=\frac{5}{3}$

$\sec x=\large\frac{OP}{OM}=\frac{5}{-4}=-\frac{5}{4}$

$\cot x=\large\frac{OM}{MP}=\frac{-4}{3}=-\frac{4}{3}$