Question

Please select the best answer from the choices provided

Answer 1

`x=(5\pi)/(4)`

Explanation:

We want to solve;

`\cscx=-√(2)` in the 3rd quadrant

Recall that;

`\sin x=(1)/(\csc x)`

We use the reciprocal ratio to get;

`\sin x=-(√(2))/(2)`

In the third quadrant the solution is

`x=\pi+\sin^(-1)((√(2) )/(2) )`

`x=\pi+(\pi)/(4)`

`x=(5\pi)/(4)`