Answer:
A
Step-by-step explanation:
We can write this as Sinx by "flipping" the [tex]-\sqrt{2}[/tex].
So we will have: [tex]Sin(x)=-\frac{1}{\sqrt{2} }[/tex]
From basic trigonometry, we know the value of [tex]\frac{1}{\sqrt{2}}[/tex] of sine is of the angle [tex]\frac{\pi}{4}[/tex]
But when is sine negative? Either in 3rd or 4th quadrant. But the answer has to be between 0 and [tex]\frac{3\pi}{2}[/tex], 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:
[tex]\frac{\pi}{4}+\pi\\=\frac{\pi +4\pi}{4}\\=\frac{5\pi}{4}[/tex]
A is the right answer.
