Browse Questions

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

$\begin{array} (A) \frac{1}{2} \quad & (B) \frac{1}{3} \quad & (C) \frac{1}{4} \quad & (D) 1 \end{array}$

Toolbox:
• $sin^{-1}(-\large\frac{1}{2})=-\large\frac{\pi}{6}$
• $sin\large\frac{\pi}{2}=1$
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$
edited May 2, 2014