Browse Questions

Find the principal values of the following: $sin^{-1} \bigg( -\frac {1} {2}\bigg)$

$\begin{array}{1 1} -\frac{\pi}{6} \\ -\frac{-\pi}{2} \\ -\frac{\pi}{4} \\ -\pi \end{array}$

Toolbox:
• Principal interval of $sinx$ is $\bigg[ \large\frac{\pi}{2}, \large\frac{\pi}{2} \bigg]$
• $cosx\: is \: [ 0, \pi ]$
• $tanx \: is \: \bigg( \large\frac{-\pi}{2}, \large\frac{\pi}{2} \bigg)$

Ans:  $\large-\frac{\pi}{6}$

edited Mar 15, 2013

Toolbox:
• The range of the principal value of $\sin^{-1}x$ is $\left [ \large-\frac{\pi}{2}, \large\frac{\pi}{2} \right ]$
Let $\sin^{-1}(\large-\frac{1}{2}) = x$
$\Rightarrow \sin x = \large-\frac{1}{2} = -\sin (\large\frac{\pi}{6}) = \sin (\large-\frac{\pi}{6})$
Therefore, $x = \large-\frac{\pi}{6}$.
edited Apr 18 by meena.p