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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 $$-\sqrt{3}$$.

1029896_1059548_ans_0a07a8ad685c4a81a144c0ff025cce87.png

Maths

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