What is the range of cosec^-1 x?

Inverse Trigonometric Functions · Question 18 of 120

Question 18

MediumOriginal question

What is the range of $\operatorname{cosec}^{-1} x$ ?

\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]

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[0, \pi] - \left\{\frac{\pi}{2}\right\}

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(0, \pi)

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\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] - \{0\}

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CorrectNot quiteAnswer D

Correct answer: D

$\operatorname{cosec}$ uses the branch of $\sin$ , $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ .
$\operatorname{cosec} 0$ is not defined, so 0 is removed.

Worth noting

$[0, \pi] - \left\{\frac{\pi}{2}\right\}$ is the range of $\sec^{-1}$ .

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

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