Question

Please select the best answer from the choices provided

Answer 1

Answer:

$x=\frac{5\pi}{4}$

Step-by-step explanation:

We want to solve;

$\cscx=-\sqrt{2}$ in the 3rd quadrant

Recall that;

$\sin x=\frac{1}{\csc x}$

We use the reciprocal ratio to get;

$\sin x=-\frac{\sqrt{2}}{2}$

In the third quadrant the solution is

$x=\pi+\sin^{-1}(\frac{\sqrt{2} }{2} )$

$x=\pi+\frac{\pi}{4}$

$x=\frac{5\pi}{4}$