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,
$\therefore \sec x=-2\Rightarrow \cos x=-\frac{1}{2}$
$\therefore {\sin }^{2}x=1-{\cos }^{2}x=1-\frac{1}{4}=\frac{3}{4}$
$\Rightarrow \sin x=\frac{-\sqrt{3}}{2}$