Read the two statements and choose the correct option. I. cos^-1(-1/2) = π - cos^-1 1/2. II. sin^-1(-1/2) = π - sin^-1 1/2.

Question 109

HardOriginal question

Read the two statements and choose the correct option.
I. $\cos^{-1}\left(-\frac{1}{2}\right) = \pi - \cos^{-1} \frac{1}{2}$ .
II. $\sin^{-1}\left(-\frac{1}{2}\right) = \pi - \sin^{-1} \frac{1}{2}$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

I: $\frac{2\pi}{3} = \pi - \frac{\pi}{3}$ . True.
II: the left side is $-\frac{\pi}{6}$ , the right $\frac{5\pi}{6}$ . False; for $\sin^{-1}$ a negative input just flips the sign.

Worth noting

The rule $\pi - \ldots$ belongs to the branch $[0, \pi]$ , not to $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ .

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