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What is the principal value of \( \cos^{-1} \bigg( -\large\frac{\sqrt 3}{2} \bigg). \)

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  • \(cos(\pi-\theta)=-cos\theta\)
We know that \(cos\frac{\pi}{6}=\frac{\sqrt3}{2}\)
\(\Rightarrow\:-\frac{\sqrt3}{2}=cos(\pi-\frac{\pi}{6})=cos\frac{5\pi}{6}\)
\(\Rightarrow\: \cos^{-1}-\frac{\sqrt3}{2}=cos^{-1}cos \bigg( \pi-\large\frac{\pi}{6} \bigg)=\large\frac{5\pi}{6}\)
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