Find the values of other five trigonometric functions if $\sin x=\frac{3}{5}$, x lies in second quadrant.
$\sin x=\frac{3}{5}$
$\operatorname{cosec} x=\frac{1}{\sin x}=\frac{1}{\left(\frac{3}{5}\right)}=\frac{5}{3}$
$\sin ^{2} x+\cos ^{2} x=1$
$\Rightarrow \cos ^{2} x=1-\sin ^{2} x$
$\Rightarrow \cos ^{2} x=1-\left(\frac{3}{5}\right)^{2}$
$\Rightarrow \cos ^{2} x=1-\frac{9}{25}$
$\Rightarrow \cos ^{2} x=\frac{16}{25}$
$\Rightarrow \cos x=\pm \frac{4}{5}$
Since $x$ lies in the $2^{\text {nd }}$ quadrant, the value of $\cos x$ will be negative
$\therefore \cos x=-\frac{4}{5}$
$\sec x=\frac{1}{\cos x}=\frac{1}{\left(-\frac{4}{5}\right)}=-\frac{5}{4}$
$\tan x=\frac{\sin x}{\cos x}=\frac{\left(\frac{3}{5}\right)}{\left(-\frac{4}{5}\right)}=-\frac{3}{4}$
$\cot x=\frac{1}{\tan x}=-\frac{4}{3}$
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