Question

Find the slope of the line, which makes an angle of ${30}^{\circ }$ with the positive direction of $y-$axis measured anticlockwise.

Answer 1

Slope of line
The line makes angle of ${30}^{\circ }$ from positive y-axis as shown in the figure.

Hence it makes angle of $({90}^{\circ }+{30}^{\circ })$ from positive x−axis i.e., ${120}^{\circ }$ from positive $x-$axis measured anti-clockwise.
Hence $\theta ={120}^{\circ }$
Slope $\left(m\right)=\tan \theta$
$=\tan {120}^{\circ }$
$=\tan ({180}^{\circ }-{60}^{\circ })$
$=-\tan {60}^{\circ }$
$\{\because \tan ({180}^{\circ }-\theta )=-\tan \theta \}$
$=-\sqrt{3}$
Hence, Slope of line $=-\sqrt{3}$.