Question:
Find the slope of the line, which makes an angle of $30^{\circ}$ with the positive direction of $y$-axis measured anticlockwise.
Solution:
If a line makes an angle of $30^{\circ}$ with the positive direction of the $y$-axis measured anticlockwise, then the angle made by the line with the positive direction of the $x$-axis measured anticlockwise is $90^{\circ}+30^{\circ}=120^{\circ}$.
Thus, the slope of the given line is $\tan 120^{\circ}=\tan \left(180^{\circ}-60^{\circ}\right)=-\tan 60^{\circ}=-\sqrt{3}$
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