Answer:
[tex]x=\frac{5\pi}{4}[/tex]
Step-by-step explanation:
We want to solve;
[tex]\cscx=-\sqrt{2}[/tex] in the 3rd quadrant
Recall that;
[tex]\sin x=\frac{1}{\csc x}[/tex]
We use the reciprocal ratio to get;
[tex]\sin x=-\frac{\sqrt{2}}{2}[/tex]
In the third quadrant the solution is
[tex]x=\pi+\sin^{-1}(\frac{\sqrt{2} }{2} )[/tex]
[tex]x=\pi+\frac{\pi}{4}[/tex]
[tex]x=\frac{5\pi}{4}[/tex]
