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Principal value of sin^-1(sin t), cos^-1(cos t), tan^-1(tan t) for t outside the principal range

This type of question, asked 5 times: May 2022 S1, 10 May 2023 S1, 13 May 2024 S2, 17 Apr 2026 S2, 19 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    125
    The principal value of sin⁡−1 ⁣(sin⁡2π3)\sin^{-1}\!\left(\sin\frac{2\pi}{3}\right) is

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  2. Question 2

    10 May 2023 S1

    127
    The value of tan⁡−1 ⁣(tan⁡7π6)\tan^{-1}\!\left(\tan\frac{7\pi}{6}\right) is

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  3. Question 3

    13 May 2024 S2

    150
    The principal value of sin⁡−1 ⁣(sin⁡3π4)\sin^{-1}\!\left(\sin\frac{3\pi}{4}\right) is:

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  4. Question 4

    17 Apr 2026 S2

    66
    cos⁡−1(cos⁡4π3)+sin⁡−1(sin⁡4π3)=…\cos^{-1}\left(\cos\dfrac{4\pi}{3}\right) + \sin^{-1}\left(\sin\dfrac{4\pi}{3}\right) = \ldots

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  5. Question 5

    19 Apr 2026 S2

    67
    The value of sin⁡−1(sin⁡5π6)+cos⁡−1(cos⁡7π6)+tan⁡−1(tan⁡2π3)\sin^{-1}\left(\sin\dfrac{5\pi}{6}\right) + \cos^{-1}\left(\cos\dfrac{7\pi}{6}\right) + \tan^{-1}\left(\tan\dfrac{2\pi}{3}\right) is equal to...

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