Question

if cosx=-3/5,x lies in the 3rd quadrant, find cosecx​

Answer 1

Step-by-step explanation:

we know that only tanx and cotx are positive in 3rd Quardent..

so sinx , cosex, etc. are negative...

So

$\sin(x) = - \sqrt{1 - {cos}^{2} x} \\ \\ = - \sqrt{1 - \frac{ {3}^{2} }{ {5}^{2} } } \\ \\ = - \sqrt{1 - \frac{9}{25} } \\ \\ = - \sqrt{ \frac{16}{25} } = - \frac{4}{5} \\ \\ cosecx = \frac{1}{ \sin(x) } = \frac{1}{ - \frac{4}{5} } = - \frac{5}{4}$

$cosecx= - \frac{5}{4}$