Question

Angle made by the line $x\cos {30}^o+y\sin {30}^o+5=0$, with the positive $X-axis$, is :

• A. $\pi /6$
• B. $2\pi /3$
• C. $5\pi /6$
• D. $\pi /3$

Answer 1

Answer: (B)

$2\pi /3$

$\text{Given}\text{that}\text{.}$

$\text{xCos3}{\text{0}}^0+\text{ySin}{30}^0+5=0$

$\Rightarrow \text{ySin}{30}^0=-\text{xCos}{30}^0-5$

$\Rightarrow \text{y}=-\text{x}\frac{\text{Cos}{30}^0}{\text{Sin}{30}^0}-\frac{5}{\text{Sin}{30}^0}$

$\Rightarrow y=-\text{x}\text{Cot}{30}^0-5\text{Cosec}{30}^0$

$\text{On}\text{Comparing}\text{that}\text{.}$

$\Rightarrow \text{y}=\text{mx}+\text{c}$

$\text{m}=-\text{Cot}{30}^0$

$m=Cot({180}^0-{30}^0)\therefore Cot({180}^0-A)=-CotA$

$m=Cot{150}^{0}m=\tan ({270}^0-{120}^0)$

$\text{We}\text{know}\text{that}$

$\text{m}\text{=}\text{tan}\theta =\tan {120}^0$

$\theta ={120}^0$

$\theta =120\times \frac{\pi }{180}$

$\theta =\frac{2\pi }{3}$

$\text{Hence,}\text{this}\text{is}\text{the}\text{answer}$