Question

Value of $\theta (0<\theta <{360}^o)$ which satisfy the equation $\text{cosec}\theta +2=0$ is:

• A. ${210}^o,{100}^o$
• B. ${240}^o,{300}^o$
• C. ${210}^o,{240}^o$
• D. ${210}^o,{330}^o$

Answer 1

Answer: (D)

${210}^o,{330}^o$

Given: $\text{cosec}\theta +2=0$

$\Rightarrow \sin \theta =-\frac{1}{2}$

$\Rightarrow \theta =(\pi +\frac{\pi }{6}),$ $(2\pi -\frac{\pi }{6})$

$\Rightarrow \theta =\frac{7\pi }{6},\frac{11\pi }{6}$

$\Rightarrow \theta ={210}^{\circ },{330}^{\circ }$