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

Inverse Trigonometric Functions · Question 37 of 120

Question 37

EasyOriginal question

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

- \frac{\pi}{6}

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\frac{\pi}{6}

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\frac{\pi}{3}

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\frac{5 \pi}{6}

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Find the angle $\theta$ in the branch $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\}$ with $\operatorname{cosec} \theta = 2$ .
That angle is $\frac{\pi}{6}$ .

Worth noting

$\frac{5\pi}{6}$ has sine $\frac{1}{2}$ too, but lies outside $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ .

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

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