Sub-topic 1
2021 · National One-Eighth
Free
Inverse of $y=\sin\left(\dfrac{x}{2}\right)$ for $-\pi\lt x\lt\pi$
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Sub-topic 2
2021 · National Preliminary
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Evaluating inverse trig functions outside the principal range (true/false)
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Sub-topic 3
2023 · National Preliminary
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Evaluating $\cos[2\cos^{-1}(x)]$ for given $x$
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Sub-topic 4
2017 · National Quarterfinal
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Is $\sin^{-1}(0)=\sin(0)$? (true/false)
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Sub-topic 5
2017 · National Quarterfinal
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Is $\cos^{-1}(0)=\cos(0)$? (true/false)
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Sub-topic 6
2017 · National Quarterfinal
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Is $\tan^{-1}(1)=\dfrac{1}{\cot^{-1}(1)}$? (true/false)
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Sub-topic 7
2022 · National Preliminary
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Does $\sin^{-1}(1)$ equal $\cos^{-1}(0)$? (true/false)
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Sub-topic 8
2022 · National Preliminary
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Does $\sin^{-1}(0)$ equal $\cos^{-1}(1)$? (true/false)
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Sub-topic 9
2022 · National Preliminary
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Does $\sin^{-1}(0.5)$ equal $\cos^{-1}(0.5)$? (true/false)
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Sub-topic 10
2023 · National Preliminary
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Does $2\cos^{-1}\left(\dfrac{1}{\sqrt2}\right)$ equal $\sin^{-1}(1)$? (true/false)
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Sub-topic 11
2023 · National Preliminary
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Does $2\cos^{-1}\left(\dfrac{\sqrt3}{2}\right)$ equal $\sin^{-1}\left(\dfrac{\sqrt3}{2}\right)$? (true/false)
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Sub-topic 12
2023 · National Preliminary
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Does $\tan^{-1}(1)$ equal $\cos^{-1}(1)$? (true/false)
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