Find the inclination of a line whose slope is

Solution:

We know that the slope of a given line is given by

Slope $=\tan \theta$ Where $\theta$ angle of inclination

(i) $\tan \theta=\sqrt{3}$

$\Rightarrow \theta=\tan ^{-1}(\sqrt{3})$

$\Rightarrow \theta=60^{\circ}$

(ii) $\tan \theta=\frac{1}{\sqrt{3}}$

$\Rightarrow \theta=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\Rightarrow \theta=30^{\circ}$

(iii) $\tan \theta=1$

$\Rightarrow \theta=\tan ^{-1}(1)$

$\Rightarrow \theta=45^{\circ}$

(iv) $\tan \theta=-1$

$\Rightarrow \theta=\tan ^{-1}(-1)$

$\Rightarrow \theta=-45^{\circ}=315^{\circ}$

(v) $\tan \theta=-\sqrt{3}$

$\Rightarrow \theta=\tan ^{-1}(-\sqrt{3})$

$\Rightarrow \theta=-60^{\circ}=300^{\circ}$