Question

If $\sec x=-2$ and $\pi < x < \frac{3 \pi}{2}$, then $\sin x$ is equal to

• A. $-\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{33}}{2}$
• C. $-\frac{1}{2}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

$\because \pi < x < \frac{3 \pi}{2}$
So, $\sin x$ is negative,
$\therefore \sec x=-2 \Rightarrow \cos x=-\frac{1}{2} $
$\therefore \sin ^2 x=1-\cos ^2 x=1-\frac{1}{4}=\frac{3}{4} $
$\Rightarrow \sin x=\frac{-\sqrt{3}}{2}$