cosec (-1110^ )=? - Vidyadip

MCQ

$\operatorname{cosec}\left(-1110^{\circ}\right)=?$

✓
$-2$
B
$\frac{-2}{\sqrt{3}}$
C
$2$
D
$\frac{2}{\sqrt{3}}$

✓

Answer

Correct option: A.

$-2$

$180^{\circ}=\pi^c$
$\Rightarrow 1110^{\circ}=\left(\frac{\pi}{180} \times 1110\right)^c=\left(\frac{37 \pi}{6}\right)^c$
$\therefore \operatorname{cosec}\left(-1110^{\circ}\right)=-\operatorname{cosec} 1110^{\circ}=-\operatorname{cosec} \frac{37 \pi}{6}$
$=-\operatorname{cosec}\left(6 \pi+\frac{\pi}{6}\right)$
$=-\operatorname{cosec} \frac{\pi}{6}$
$=-2$
$[\because \operatorname{cosec}(2 n \pi+\theta)=\operatorname{cosec} \theta]$

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