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Inverse Trigonometric Functions · Question 119 of 120

Match each expression in List I with its value in List II.

Question 119

HardOriginal question

Match each expression in List I with its value in List II.

List IList II
A. sin⁡−1(sin⁡3)\sin^{-1}(\sin 3)I. 2π−42\pi - 4
B. cos⁡−1(cos⁡4)\cos^{-1}(\cos 4)II. π−3\pi - 3
C. tan⁡−1(tan⁡2)\tan^{-1}(\tan 2)III. π−1\pi - 1
D. cot⁡−1(cot⁡(−1))\cot^{-1}\left(\cot(-1)\right)IV. 2−π2 - \pi
Options for question 119

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. sin⁡(π−3)=sin⁡3\sin(\pi - 3) = \sin 3 with π−3\pi - 3 in [−π2,π2]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]; cos⁡(2π−4)=cos⁡4\cos(2\pi - 4) = \cos 4 with 2π−42\pi - 4 in [0,π][0, \pi].

  2. tan⁡(2−π)=tan⁡2\tan(2 - \pi) = \tan 2 with 2−π2 - \pi in (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right); cot⁡(π−1)=cot⁡(−1)\cot(\pi - 1) = \cot(-1) with π−1\pi - 1 in (0,π)(0, \pi).

Worth noting

Swapping the values of sin⁡−1(sin⁡3)\sin^{-1}(\sin 3) and cos⁡−1(cos⁡4)\cos^{-1}(\cos 4) forgets where 4 lies: it is between π\pi and 2π2\pi, so the angle on [0,π][0, \pi] with the same cosine is 2π−42\pi - 4.

Concept
An inverse function applied to a function
Typical time
150 s
Your time
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The rule this testsValues of expressions
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Ten questions from Inverse Trigonometric Functions, at your own pace.

Practise this chapter →

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