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Find the values of each of the expressions in \( sin \bigg(\frac{\pi}{3} - sin^{-1} ( -\frac{1}{2} ) \bigg) \) is equal to

\[ \begin{array} (A) \frac{1}{2} \quad & (B) \frac{1}{3} \quad & (C) \frac{1}{4} \quad & (D) 1 \end{array} \]
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  • \(sin^{-1}(-\large\frac{1}{2})=-\large\frac{\pi}{6}\)
  • \(sin\large\frac{\pi}{2}=1\)
Given $sin \bigg(\large\frac{\pi}{3} - sin^{-1} ( -\large\frac{1}{2} ) \bigg)$:
We know that \(sin^{-1}(-\large\frac{1}{2})=-\large\frac{\pi}{6}\).
Therefore, $\sin \bigg(\large\frac{\pi}{3} - \normalsize\sin^{-1} ( -\large\frac{1}{2} ) \bigg) = $ \( \sin \bigg[ \large\frac{\pi}{3}- \bigg( -\large\frac{\pi}{6} \bigg) \bigg] \)\(= \normalsize \sin\large\frac{\pi}{2} \)\(=1\)
answered Feb 23, 2013 by thanvigandhi_1
edited May 2, 2014 by balaji.thirumalai
 
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