Question

Evaluate :
i) ${\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
ii) ${\sin }^{-1}(-\frac{1}{2})$

Answer 1

(1)

Let $ta{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)=x$

then,

$tanx=\frac{1}{\sqrt{3}}$

$tanx=tan\left(\frac{\pi }{6}\right)$

$\Rightarrow x=\frac{\pi }{6}$

$ta{n}^{-1}\left(\frac{1}{\sqrt{3}}\right)=\frac{\pi }{6}$

(2)

Let $si{n}^{-1}(-\frac{1}{2})=x$

then,

$sinx=-\frac{1}{2}$

$sinx=sin(-\frac{\pi }{6})$

$\Rightarrow x=-\frac{\pi }{6}$

$si{n}^{-1}(-\frac{1}{2})=-\frac{\pi }{6}$