Answer
$\frac{2\pi}{3}$
Work Step by Step
Step 1. Evaluate $f(-\frac{\pi}{6})=sin(-\frac{\pi}{6})=-\frac{1}{2}$
Step 2. Evaluate $g^{-1}(f(-\frac{\pi}{6}))=cos^{-1}(-\frac{1}{2})=\frac{2\pi}{3}$
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