The figure shows the graph of a function through (-1, π), (0, π/2) and (1, 0), defined only on [-1, 1]. Which function is it? A curve falling from (−1, π) through (0, π/2) to (1, 0)

The figure shows the graph of a function…

The figure shows the graph of a function through (-1, π), (0, π/2) and (1, 0), defined only on [-1, 1].

Question 72

MediumOriginal question

The figure shows the graph of a function through $(-1, \pi)$ , $\left(0, \frac{\pi}{2}\right)$ and $(1, 0)$ , defined only on $[-1, 1]$ . Which function is it?

A curve falling from (−1, π) through (0, π/2) to (1, 0)

y = \sin^{-1} x

Correct answerYour answer

y = \cot^{-1} x

Correct answerYour answer

y = \tan^{-1} x

Correct answerYour answer

y = \cos^{-1} x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Defined only on $[-1, 1]$ : $\sin^{-1}$ or $\cos^{-1}$ .
It falls from $\pi$ to 0, and $\cos^{-1} 1 = 0$ , $\cos^{-1}(-1) = \pi$ : it is $\cos^{-1} x$ .

Worth noting

$\sin^{-1} x$ rises, from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ .

Concept: Recognising an inverse function from its graph
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsGraphs of the inverse functions

Practise this chapter →

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

Practise this chapter →

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

The figure shows the graph of a function through (-1, π), (0, π/2) and (1, 0), defined only on [-1, 1].

Question 72

Explanation