For which values of x does this curve y =…

For which values of x does this curve y = cot^-1 x lie below the line y = π/3?

Question 81

HardOriginal question

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

For which values of $x$ does this curve $y = \cot^{-1} x$ lie below the line $y = \frac{\pi}{3}$ ?

x > \frac{1}{\sqrt{3}}

Correct answerYour answer

x < \frac{1}{\sqrt{3}}

Correct answerYour answer

x > \sqrt{3}

Correct answerYour answer

0 < x < \frac{1}{\sqrt{3}}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The curve meets the line where $x = \cot \frac{\pi}{3} = \frac{1}{\sqrt{3}}$ .
The curve falls as $x$ increases, so it is below the line to the right of that point: $x > \frac{1}{\sqrt{3}}$ .

Worth noting

$x < \frac{1}{\sqrt{3}}$ treats the curve as rising; to the left of the meeting point it is above the line.

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

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