Question

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

Answer 1

Clearly $\sin x=\sqrt{1-\frac{9}{25}}$

$\sin x=\pm \frac{4}{5}$

Since x is in 3rd quadrant, $\sin x=-\frac{4}{5}$

$cosec$ $x=-\frac{5}{4}$

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

$\tan x=\frac{4}{3}$

$\cot x=\frac{3}{4}$