What is the principal value of cosec^-1(- (2 √(3))/3)?

Inverse Trigonometric Functions · Question 54 of 120

Question 54

MediumOriginal question

What is the principal value of $\operatorname{cosec}^{-1}\left(- \frac{2 \sqrt{3}}{3}\right)$ ?

- \frac{\pi}{3}

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- \frac{\pi}{6}

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\frac{\pi}{3}

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\frac{4 \pi}{3}

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CorrectNot quiteAnswer A

Correct answer: A

Find the angle $\theta$ in the branch $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\}$ with $\operatorname{cosec} \theta = - \frac{2 \sqrt{3}}{3}$ .
That angle is $- \frac{\pi}{3}$ .

Worth noting

$\operatorname{cosec}\frac{4\pi}{3} = -\frac{2}{\sqrt{3}}$ too, but the branch is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ .

Ten questions from Inverse Trigonometric Functions, at your own pace.

Ten questions from Inverse Trigonometric Functions, at your own pace.