[中學] 反三角函數定義
關於 arcsec, arccsc 的值域有點疑問
http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
用 arcsec 為例好了, 維基上的值域是 0≦y≦π, y≠π/2
我們老師也是這樣講的
但 James Stewart 卻在《CALCULUS:Early Transcedentals》中寫說
arcsec 的值域是 [0,π/2)∪[π,π3/2), 而且說
"The choice of intervals of y in the definitions of arccsc and
arcsec is not universally agreed upon."
真的是這樣嗎 !?
1
而且他在這本書中給出的 arcsec(x) 的導函數也是 -------------- ...
x√(x^2 - 1)
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