Question

Csc x= -√2 for π≤x≤3π/2

Answer 1

Answer:

A

Step-by-step explanation:

We can write this as Sinx by "flipping" the $-\sqrt{2}$.

So we will have:  $Sin(x)=-\frac{1}{\sqrt{2} }$

From basic trigonometry, we know the value of  $\frac{1}{\sqrt{2}}$  of sine is of the angle $\frac{\pi}{4}$

But when is sine negative? Either in 3rd or 4th quadrant. But the answer has to be between 0 and  $\frac{3\pi}{2}$, so we disregard 4th quadrant.

To get the angle in 3rd quadrant, we add π to the acute angle of the first quadrant (which is π/4 in our case). Thus we have:

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

A is the right answer.