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

Inverse Trigonometric Functions · Question 32 of 120

Question 32

EasyOriginal question

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

- \frac{\pi}{3}

Correct answerYour answer

- \frac{\pi}{6}

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\frac{\pi}{6}

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\frac{7 \pi}{6}

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Find the angle $\theta$ in the branch $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ with $\sin \theta = - \frac{1}{2}$ .
That angle is $- \frac{\pi}{6}$ .

Worth noting

$\frac{7\pi}{6}$ 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.