Sine of the times.
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06-22-2024, 08:42 PM
Post: #21
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RE: Sine of the times.
(06-12-2024 08:58 PM)Nigel (UK) Wrote: Gauss found this odious, because he felt that \(\sin^2(x)\) should mean \(\sin(\sin(x))\) (and he has a point!) but since the repeated sine is used so rarely this isn't an issue in practice. Some years ago I had a German student who told me that in Germany, they are taught that \(f^2(x)\) means \(f(f(x))\). When I asked her about \(\sin^2(x)\) she said that trig functions were special exceptions. I thought this was rather odd until it occurred to me that this is exactly what we do with derivatives: \({d^2\over dx^2} f(x)\) means \({d\over dx}{d\over dx} f(x)\). The point you make about \(\sin^{-1}x\) is consistent with this notation. The nth derivative is often denoted \(f^{(n)}(x)\) with the n in parentheses. Using this notation, I have seen \(f^{(0)}(x)\) (the zeroth derivative) to mean \(f(x)\) and \(f^{(-1)}(x)\) (the inverse derivative) to mean the antiderivative of \(f(x)\). |
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06-22-2024, 08:55 PM
Post: #22
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RE: Sine of the times. | |||
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