Principal value of ${cos}^{- 1} (- 1 / 2)$ is equal to

π / 3

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2 π / 3

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- π / 3

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- 2 π / 3

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Solution

The correct option is D $2 π / 3$
${cos}^{- 1} (- 1 / 2) = π - {cos}^{- 1} (1 / 2)$
$= π - \frac{π}{3} = \frac{2 π}{3}$

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Similar questions

- 1 + \sqrt{- 3} = r e^{θ}

If -1+ $\sqrt{- 3}$ =r $e^{i θ}$ , then $θ$ is equal to

z

C o l u m n - I

a r g (z)

c o l u m n - I I

$C o l u m n - I$ (equation in z)	$C o l u m n - I I$ (principal value of arg(z))
$z^{2} - z + 1 = 0$	$- 2 π / 3$
$z^{2} + z + 1 = 0$	$- π / 3$
${2 z}^{2} + 1 + i \sqrt{3} = 0$	$π / 3$
${2 z}^{2} + 1 - i \sqrt{3} = 0$	$2 π / 3$

{sin}^{- 1} x - {sin}^{- 1} y = \frac{2 π}{3}; {cos}^{- 1} x - {cos}^{- 1} = \frac{π}{3}

(a) [\frac{π}{2}, \frac{3 π}{2}] (b) [π, 2 π] - \{\frac{3 π}{2}\} (c) (0, π) (d) [2 π, 3 π]

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