Question

The domain of $f\left(x\right)=\log \left(\sin x\right)$ is

• A. $(-\pi ,\pi )$
• B. $(2n\pi ,(2n+1\left)\pi \right)$ and $n\in Z$
• C. $[0,2\pi ]$
• D. $(-\frac{\pi }{2},\frac{\pi }{2})$

Answer 1

The correct option is B $(2n\pi ,(2n+1\left)\pi \right)$ and $n\in Z$

$\log x$ is defined only for $x>0$
$\therefore$ $\sin x>0$
$\Rightarrow x\in (2n\pi ,(2n+1\left)\pi \right)\forall n\in Z$