Question

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

Solution

$$\Rightarrow$$  The line makes angle of $$30^o$$ from positive $$y-axis$$$$\Rightarrow$$  Hence, it makes angles of $$(90^o+30^o)$$ from positive x axis $$i.e.$$ $$120^o$$ from positive $$x-axis$$$$\therefore$$   $$\theta=120^o$$$$\Rightarrow$$$$Slope=m=\tan\theta$$                          $$=\tan\,120^o$$                          $$=\tan(180^o-60^o)$$                          $$=-\tan\,60^o$$                          $$=-\sqrt{3}$$$$\therefore$$  Slope of the line is $$-\sqrt{3}$$.Maths

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