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

Inverse Trigonometric Functions · Question 49 of 120

Question 49

MediumOriginal question

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

- \frac{\pi}{3}

Correct answerYour answer

\frac{\pi}{3}

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\frac{2 \pi}{3}

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\frac{4 \pi}{3}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

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

Worth noting

$\sec^{-1}$ takes the branch of $\cos^{-1}$ , $[0, \pi]$ , so the angle is $\pi - \frac{\pi}{3}$ .

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

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