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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} $

Can you answer this question?
 
 

2 Answers

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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:  \(\large-\frac{\pi}{6}\)

answered Feb 22, 2013 by thanvigandhi_1
edited Mar 15, 2013 by thanvigandhi_1
 
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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, $x = \large-\frac{\pi}{6}$.
answered Mar 1, 2013 by balaji.thirumalai
edited Apr 18 by meena.p
 
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