Question

Number of solutions of the equation $2 \sin (\{x\})=1$ in $x \in[0,2 \pi]$ is equal to
[Note: $\{k\}$ denotes fractional part of $k$.]

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (C)

$2 \sin \{x\}=1 $
$\sin \{x\}=1 / 2$
$\{x\}=\pi / 6 \text { is the only value }$
$x=\frac{\pi}{6}, \frac{\pi}{6}+1, \frac{\pi}{6}+2, \frac{\pi}{6}+3,4+\frac{\pi}{6}, 5+\frac{\pi}{6} \Rightarrow 6$