How does this curve y = cot^-1 x behave as x…

How does this curve y = cot^-1 x behave as x increases?

Question 67

EasyOriginal question

Consider the curve $y = \cot^{-1} x$ , defined for every real $x$ , with its values on the principal branch $(0, \pi)$ .

How does this curve $y = \cot^{-1} x$ behave as $x$ increases?

It rises all the way as

x

increases.Correct answerYour answerIt rises up to

x = 0

, then falls.Correct answerYour answerIt falls all the way as

x

increases.Correct answerYour answerIt falls up to

x = 0

, then rises.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

On $(0, \pi)$ , $\cot \theta$ falls as $\theta$ grows, taking each real value once.
So a larger $x$ needs a smaller angle: $\cot^{-1} x$ falls as $x$ increases, everywhere.

Worth noting

The rising curve is $y = \tan^{-1} x$ ; $\cot^{-1}$ undoes a falling function, so it falls too.

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

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