Which of the following statements are true?
I. $\sin^{-1} x$ is increasing on $[-1, 1]$ .
II. $\cos^{-1} x$ is decreasing on $[-1, 1]$ .
III. The curve $y = \cot^{-1} x$ passes through the origin.
IV. The curve $y = \sin^{-1} x$ is the mirror image of $y = \sin x$ , $-\frac{\pi}{2} \le x \le \frac{\pi}{2}$ , in the line $y = x$ .

I, II and IV onlyCorrect answerYour answerAll four: I, II, III and IVCorrect answerYour answerI and II onlyCorrect answerYour answerI and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I, II and IV are true: an inverse keeps the direction of the branch it undoes, and its graph is that branch reflected in $y = x$ .
III is false: $\cot^{-1} 0 = \frac{\pi}{2}$ , so the graph meets the $y$ -axis at $\left(0, \frac{\pi}{2}\right)$ .

Worth noting

III mixes $\cot^{-1}$ with $\tan^{-1}$ , which does pass through the origin.

Concept: Facts about the graphs
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsGraphs of the inverse functions

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

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