Question:
Find the equation of the line for which
$p=3$ and $\propto=2250$
Solution:
Given: $p=3$ and $\alpha=2250$
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:
$x \cos \alpha+y \sin \alpha=p$
$x \cos 2250+y \sin 2250=3$
i.e; $\cos 2250=\cos ((6 \times 360)+90)=\cos ((6 \times 2 \pi)+90)=\cos 90$
similarly, $\sin 2250=\sin ((6 \times 60)+90)=\sin ((6 \times 2 \pi)+90)=\sin 90$
hence, $x \cos 90+y \sin 90=3$
$x \times(0)+y \times 1=3$
Hence The required equation of the line is y=3.