Question

If $\cos x=\frac{-3}{5}$, $x$ lies in the third quadrant. Find the values of other five trigonometric function ?

Answer 1

$\cos x=\frac{-3}{5}$

$x$ is in $3^{rd}$ quadrant

in $3^{rd}$ quadrant only $\tan$ and $\cot$ are positive

$⟹\sin x=\frac{-4}{5}\tan x=\frac{4}{3}\cot x=\frac{3}{4}\sec x=\frac{-5}{3}\csc x=\frac{-5}{4}$