Which of the following is the principle value of ${cos}^{- 1} (\frac{- 1}{2})$ ?

\frac{π}{3}

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\frac{π}{6}

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\frac{2 π}{3}

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\frac{3 π}{2}

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Solution

The correct option is C $\frac{2 π}{3}$
Given,

${cos}^{- 1} (- \frac{1}{2})$

$= {cos}^{- 1} (- cos 60)$

$= {cos}^{- 1} [cos (180 - 60)]$

$= 120$

$= \frac{2 π}{3}$

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