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Model Paper 6 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 61 Mark
MCQ
$\operatorname{cosec}\left(-1110^{\circ}\right)=?$
  • A
    -2
  • B
    $\frac{-2}{\sqrt{3}}$
  • C
    2
  • D
    $\frac{2}{\sqrt{3}}$
✓

Answer

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

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