EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Inverse Trigonometric Functions · Question 82 of 120

Match each curve in List I with the horizontal line or lines in List II that it gets ever closer to but…

Question 82

HardOriginal question

Match each curve in List I with the horizontal line or lines in List II that it gets ever closer to but never meets.

List IList II
A. y=tan⁡−1xy = \tan^{-1} xI. y=0y = 0 only
B. y=cot⁡−1xy = \cot^{-1} xII. y=π2y = \frac{\pi}{2} only
C. y=sec⁡−1xy = \sec^{-1} xIII. y=0y = 0 and y=πy = \pi
D. y=cosec⁡−1xy = \operatorname{cosec}^{-1} xIV. y=−π2y = -\frac{\pi}{2} and y=π2y = \frac{\pi}{2}
Options for question 82

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. tan⁡−1\tan^{-1} and cot⁡−1\cot^{-1} are defined for every xx; as x→±∞x \to \pm\infty they approach the open ends of their ranges, ±π2\pm\frac{\pi}{2} and 0,π0, \pi.

  2. As ∣x∣\lvert x \rvert grows, 1x→0\frac{1}{x} \to 0: sec⁡−1x=cos⁡−11x→π2\sec^{-1} x = \cos^{-1} \frac{1}{x} \to \frac{\pi}{2} and cosec⁡−1x=sin⁡−11x→0\operatorname{cosec}^{-1} x = \sin^{-1} \frac{1}{x} \to 0, the one value each range leaves out.

Worth noting

Swapping sec⁡−1\sec^{-1} and cosec⁡−1\operatorname{cosec}^{-1} forgets which value each range leaves out: π2\frac{\pi}{2} for sec⁡−1\sec^{-1}, 0 for cosec⁡−1\operatorname{cosec}^{-1}.

Concept
Rising, falling and the lines a curve approaches
Typical time
150 s
Your time
—
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.

Practise this chapterAll 120 questions in Inverse Trigonometric FunctionsRevise the notes for Inverse Trigonometric Functions