Question

If $\sin x=\frac{1}{2}$, then the value of $\tan x,x\in (\frac{\pi }{2},\pi )$ is

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

Answer 1

The correct option is B $\frac{-1}{\sqrt{3}}$

$\sin \theta =\frac{1}{2}\Rightarrow \sin \theta =\sin {30}^{\circ }\Rightarrow \sin \theta =\sin ({180}^o-{30}^o)\Rightarrow \sin \theta =\sin {150}^o$
$\therefore \theta ={150}^0$
So $\tan {150}^{\circ }=\tan ({180}^o-{30}^o)=-\tan {30}^o=-\frac{1}{\sqrt{3}}$.