Question

Find the slope of the line which makes an angle of ${30}^o$ with positive directions of the $Y-$axis measured anti-clockwise.

Answer 1

We have,

The line makes angle of ${30}^o$ from positive Y-axis.

Hence, it makes angle of $({90}^o+{30}^o)$ from positive X-axis.

i.e. ${120}^o$ from positive X-axis.

Hence, $\theta ={120}^o$

Now, we know that,

slope$=m=\tan \theta$

$m=\tan {120}^o$

$=\tan ({180}^o-{60}^o)\therefore \tan ({180}^o-\theta )=-\tan \theta$

$=-\tan {60}^o$

$=-\sqrt{3}$

Hence, this is the answer.