Question

Let $f\left(x\right)=\sin \left({\tan }^{-1}x\right)$. Then $\left[f\right(-\sqrt{3}\left)\right],$ where $[\cdot ]$ denotes the greatest integer function, is

• A. $-\frac{\sqrt{3}}{2}$
• B. $0$
• C. $-1$
• D. none of these

Answer 1

Answer: (C)

$-1$

$\left[f\right(-\sqrt{3}\left)\right]$
$=\left[\sin \right({\tan }^{-1}(-\sqrt{3})\left)\right]$
$=\left[\sin \right(-\frac{\pi }{3}\left)\right]$
$=[-\sin (\frac{\pi }{3}\left)\right]$
$=[-\frac{\sqrt{3}}{2}]$
$=[-0.866]$
$=-1$