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

Inverse Trigonometric Functions · Question 45 of 120

Question 45

MediumOriginal question

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

- \frac{\pi}{6}

Correct answerYour answer

\frac{\pi}{6}

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\frac{5 \pi}{6}

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\frac{7 \pi}{6}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Find the angle $\theta$ in the branch $[0, \pi]$ with $\cos \theta = - \frac{\sqrt{3}}{2}$ .
That angle is $\frac{5 \pi}{6}$ .

Worth noting

$\cos^{-1}$ never gives a negative angle: its branch is $[0, \pi]$ , so it is $\pi - \frac{\pi}{6}$ .

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

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