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Linguistic Trigonometry
04-18-2019, 03:21 AM
Post: #4
RE: Linguistic Trigonometry
(04-17-2019 10:41 PM)ijabbott Wrote:  I was always confused (not really, but I found it inconsistent), that \(\sin^{-1}(x)\) denoted \(\rm{asin(}x)\), but \(\sin^2(x)\) denoted \((\sin(x))^2\).

The American textbook that I currently use to teach Precalculus uses both \(\sin^{-1}(x)\) and \(\rm{arcsin(}x)\), but mostly \(\sin^{-1}(x)\). When I was a student, our textbook also defined \(\rm{Sin^{-1}(x)}\) as the inverse function (range from -pi/2 to pi/2) and \(\sin^{-1}(x)\) as the inverse relation of \(\sin(x)\) (range from -infinity to infinity).

When discussing the meaning of \(f^{-1}(x)\), I always feel like I have to apologize to the students for the confusing notation as \(f^{-1}(x)\) means inverse but \(f^{2}(x)\) means \((f(x))^2\). I sometimes ask them what \(f^{-2}(x)\) would mean and then say that I don't know either. It could be the square of the inverse or the square of the reciprocal. What if you wanted the reciprocal of the inverse? :-)

I once had a German student who said that she was taught that \(f^{2}(x) = f(f(x))\). I thought that was silly until I realized that we use this notation for \(d^2/dx^2 (f(x)) = d/dx(d/dx (f(x)))\).

This was the same student who introduced me to the (not greater than) symbol (also known as ≤ ).
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Messages In This Thread
Linguistic Trigonometry - DrD - 04-17-2019, 10:29 AM
RE: Linguistic Trigonometry - cdmackay - 04-17-2019, 10:32 PM
RE: Linguistic Trigonometry - ijabbott - 04-17-2019, 10:41 PM
RE: Linguistic Trigonometry - Wes Loewer - 04-18-2019 03:21 AM
RE: Linguistic Trigonometry - Albert Chan - 04-18-2019, 11:57 AM
RE: Linguistic Trigonometry - parisse - 04-19-2019, 04:53 AM
RE: Linguistic Trigonometry - DrD - 04-19-2019, 10:24 AM
RE: Linguistic Trigonometry - Joe Horn - 04-20-2019, 07:42 AM



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