Find the equation of the line for which

Given: p = 2 and ∝ = 3000

Here $p$ is the perpendicular that makes an angle $\propto$ with positive direction of $x$-axis, hence the equation of the straight line is given by:

Formula used:

$x \cos \alpha+y \sin \alpha=p$

$x \cos 3000+y \sin 3000=2$

i.e; $\cos 3000=\cos ((8 \times 360)+120)=\cos ((8 \times 2 \pi)+120)=\cos 120=\cos (180-60)=\cos 60$

similarly, $\sin 3000=\sin ((8 \times 360)+120)=\sin ((8 \times 2 \pi)+120)=\sin 120$

$=\sin (180-60)=-\sin 60$

hence, $x \cos 60+y(-\sin 60)=2$

$x \times(1 / 2)-y \times(\sqrt{3} / 2)=2$

Hence The required equation of the line is $x-\sqrt{3} y=4$